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["LINE RQ","Y=RY+TSP*(QX-RX)",null,null,"QRPX PARALLELOGRAMM",null,null,"TSP",{"$f":"yp/(xp+CC)","v":0.35887485844697714},"TANGENT OF SP",null,"SP",{"$f":"-CC","v":-7.0710678118654746},0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"focy",{"$f":"1/(4*foc)","v":1.25},"vpe",{"$f":"30","v":30},{"$f":"(SQRT(1+0))^3*2*foc","v":0.4},null,null,null,null,null,null,1,2,3,4,5,6,7,8,{"$f":"BJ1+1","v":9},{"$f":"BK1+1","v":10},11,12,13,14,15,16,17]
[null,"QX^2/A^2+(RY^2+T^2*(QX^2+RX^2-2QX*RX)/B^2)+2*RY*T*QX/b^2-2*T*RY*RX/B^2=1",null,null,null,null,null,null,null,"Q_V",{"$f":"SQRT((Q_X-V_X)^2+(Q_Y-V_Y)^2)","v":3.8287715008578815},"P",{"$f":"xp","v":7},{"$f":"yp","v":5.0497524691810387},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0,0,"Lpe",{"$f":"vpe*rhzero","v":12},{"$f":"focy","v":1.25},null,null,null,null,null,null,null,"t","x","y","ρ","r","tank","rx/r","ry/r","kx","ky","cosω","V","F",null,"kenx","keny","kenxky","kenyky","rkykloy","shmx","shmy","m",2]
[null,"QX^2*(1/A^2+T^2/B^2)-2QX*(t*RX-RY)*t/B^2+(T*RY-RX)^2/B^-1=0",null,null,null,"qx ",null,null,null,"p_V",{"$f":"SQRT((xp-V_X)^2+(yp-V_Y)^2)","v":0.88313366906597102},"RQ",{"$f":"RX","v":4.0999999999999996},{"$f":"RY","v":7.0597519814236884},null,null,null,null,null,"Cut of two lines y=y1+t1*(x-x1)",null,null,"SSAA","=Y2-Y1+X1*T1-X2*T2",null,"FIND E","T1",{"$f":"TSP","v":0.35887485844697714},"X1",{"$f":"-CC","v":-7.0710678118654746},"Y1",{"$f":"0","v":0},null,null,"vimata2",3,{"$f":"\" STEPS = \"&TEXT(vimata2,\"0\")","v":" STEPS = 3"},null,null,null,null,null,null,0,{"$f":"foc","v":0.2},null,null,null,null,null,null,null,null,null,{"$f":"IF(ABS($BD3-xr)<0.000001,1,0)","v":0},-5,{"$f":"2*foc*BD3","v":-2},{"$f":"foc*BD3^2","v":5},{"$f":"(SQRT(1+$BD3^2))^3*2*foc","v":53.029802941364949},{"$f":"SQRT(BE3^2+(BF3-foc)^2)","v":5.2},{"$f":"-1/BD3","v":0.2},{"$f":"$BE3/$BH3","v":-0.38461538461538458},{"$f":"($BF3-focy)/$BH3","v":0.72115384615384615},{"$f":"1/SQRT(1+$BI3^2)","v":0.98058067569092011},{"$f":"$BI3*$BL3","v":0.19611613513818404},{"$f":"($BJ3*$BL3+$BK3*$BM3)","v":-0.23571650857954804},{"$f":"Lpe/($BH3*$BN3)","v":-9.7901174660981489},{"$f":"BO3^2/(BN3*BG3)","v":-7.6677120000000079},{"$f":"BP3/$BH3^(-1.5)","v":-90.922382607032787},{"$f":"IF($BE3>0,-ABS($BE3+$BG3*$BL3),ABS($BE3+$BG3*$BL3))","v":49.999999999999986},{"$f":"ABS($BF3+$BG3*ABS($BM3))","v":15.399999999999999},{"$f":"VLOOKUP(1,BC3:BS103,16,FALSE)","v":0.13720000000000049},{"$f":"VLOOKUP(1,BC3:BT103,17,FALSE)","v":0.69400000000000073},{"$f":"VLOOKUP(1,BC3:BU103,5,FALSE)","v":0.72751071469772954},{"$f":"VLOOKUP(1,BC3:BV103,3,FALSE)","v":-0.28000000000000042},{"$f":"VLOOKUP(1,BC3:BW103,4,FALSE)","v":9.8000000000000267E-2},null,"F*f^m"]
[null,"ALFA",{"$f":"1/AA^2+(TSP/BB)^2","v":1.2575823280506758E-2},"Q_X",{"$f":"(-BETA+SQRT(BETA^2-ALFA*GAMA))/ALFA","v":3.1369662545765573},"QX//RP",null,null,null,"v_G",{"$f":"SQRT((V_X-GX)^2+(V_Y-GY)^2)","v":16.379542832566099},null,{"$f":"Q_X","v":3.1369662545765573},{"$f":"Q_Y","v":6.7141433823551884},"T_X",null,"T_Y",null,null,null,"y=y2+t2*(x-x2)",null,"XLSH","=SSAA/(T1-T2)",null,null,"T2",{"$f":"TAN(PSI)","v":-0.69310328008367272},"X2",{"$f":"-XD","v":7.141428428542846},"Y2",{"$f":"-YD","v":-4.9497474683058353},null,null,22,105,null,null,null,null,null,null,null,null,"deltt",null,null,null,null,null,null,null,null,null,0,{"$f":"BD3+deltt","v":-4.9000000000000004},-1.9600000000000002,4.8020000000000014,50.030002999800047,5.0020000000000007,{"$f":"-1/BD4","v":0.2040816326530612},{"$f":"$BE4/$BH4","v":-0.39184326269492203},0.71011595361855273,{"$f":"1/SQRT(1+$BI4^2)","v":0.97980405878040677},{"$f":"$BI4*$BL4","v":0.19996001199600136},{"$f":"($BJ4*$BL4+$BK4*$BM4)","v":-0.241934824590124},-9.9160606081030966,{"$f":"BO4^2/(BN4*BG4)","v":-8.1236168195285803},{"$f":"BP4/$BH4^(-1.5)","v":-90.8792974855522},{"$f":"IF($BE4>0,-ABS(-$BE4+$BG4*$BL4),ABS($BE4+$BG4*$BL4))","v":47.05960000000001},{"$f":"ABS($BF4+$BG4*ABS($BM4))","v":14.806000000000003},{"$f":"-PI()","v":-3.1415926535897931},{"$f":"kenxky+rhoky*COS($BT4)","v":-0.59031071469772911},{"$f":"kenyky+rhoky*SIN($BT4)","v":0.69400000000000062},{"$f":"$BJ4^2+$BK4^2","v":0.65780581010298822},null,null,{"$f":"$BP4*$BH4^m","v":-203.2529253190724}]
[null,"BETA",{"$f":"-(RX*TSP-RY)*TSP/BB^2","v":4.011047441000614E-2},"Q_Y",{"$f":"RY+TSP*(Q_X-RX)","v":6.7141433823551884},5,9,null,null,"PV∙VG",{"$f":"P_V*V_G","v":14.465325759347326},"FIND QT",{"$f":"yp-Q_Y+(-1/TSP)*Q_X-TSP*xp","v":-12.91762949397209},"XLYSH",{"$f":"M5/(-1/TSP-TSP)","v":4.1068823037098747},"YLYSH",{"$f":"Q_Y+(-1/TSP)*(O5-Q_X)","v":4.0114852654544748},null,null,"BC",null,null,null,null,null,null,"SSAA",{"$f":"-YD-0+(-CC)*TSP-(-XD)*TAN(PSI)","v":-2.5376284600521988},"XLYSH",{"$f":"AB5/(TSP-TAN(PSI))","v":-2.4122444821872726},"YLYSH",{"$f":"TSP*(EX+CC)","v":1.6719345629677396},null,null,22,105,null,null,null,null,null,null,null,null,{"$f":"0.1","v":0.1},"foc",0.2,null,null,null,null,null,null,null,0,-4.8000000000000007,-1.9200000000000004,4.6080000000000014,47.147827545285701,4.8080000000000016,0.20833333333333331,-0.3993344425956738,0.6984193011647255,0.97898041973760508,0.20395425411200105,-0.24849501260151871,-10.043824381398098,-8.6103113865113414,-90.774851312069458,44.236800000000009,14.224000000000004,{"$f":"BT4+PI()/50","v":-3.0787608005179972},-0.58887513848628825,0.64831922426098809,{"$f":"$BJ5^2+$BK5^2","v":0.64725751728262104},null,null,-199.04339731963424]
[null,"GAMA",{"$f":"(TSP*RX-RY)^2/BB^2-1","v":-0.37540351872305522},null,null,5,0,null,null,"PV∙VG/QV²",{"$f":"K5/K2^2","v":0.98675496688741748},"QT",{"$f":"Q_X","v":3.1369662545765573},{"$f":"Q_Y","v":6.7141433823551884},null,null,null,null,null,{"$f":"0","v":0},{"$f":"BB","v":7.0710678118654755},null,null,null,null,null,null,null,null,"E",null,"EY",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0,-4.7000000000000011,-1.8800000000000006,4.4180000000000019,44.380878096765976,4.6180000000000012,0.21276595744680846,-0.4071026418362928,0.68601126028583825,0.9781059289848355,0.20810764446485858,-0.25542532023101311,-10.173335590741534,-9.1299185816732837,-90.604088892614769,41.529200000000017,13.654000000000003,{"$f":"BT5+PI()/50","v":-3.0159289474462012},-0.58457407541541961,0.60281872967425609,0.63634401022905307,null,null,-194.70394979895235]
[null,null,null,null,null,null,null,null,null,"CP^2/CD^2",{"$f":"AAT^2/BBT^2","v":0.98675496688741759},null,{"$f":"T_X","v":4.1068823037098747},{"$f":"T_y","v":4.0114852654544748},"V_X",null,"V_Y",null,null,0,0,null,null,null,null,null,null,null,null,{"$f":"EX","v":-2.4122444821872726},{"$f":"EY","v":1.6719345629677396},null,"y=tanf*(x-x0)-1/2g*(x-x0)^2/vx^2=-x^2/(2*vx^2)*g+(g/vx^2*x0+tanf)*x-1/xg*x0^2/vx^2-tanf*x0",null,null,null,null,null,null,null,null,null,"SRQ = YR - YQ + XQ * taNFq - XR * taNFR: Xv = SRQ / (taNFq - taNFR): Yv = YQ + taNFq * (Xv - XQ)",null,null,null,null,null,null,null,null,null,null,null,0,-4.6000000000000014,-1.8400000000000007,4.2320000000000029,41.726756300484254,4.432000000000003,0.21739130434782603,-0.41516245487364611,0.67283393501805078,0.97717636392280094,0.21242964433104361,-0.26275706458095238,-10.304504016875434,-9.6846774018425705,-90.361781900597435,38.934400000000025,13.096000000000005,-2.9530970943744053,-0.57742449981609556,0.55767808590473988,0.62506536804858681,null,null,-190.23247676569076]
[null,null,null,"If the body is on P, we draw the conjugate diameters GP and DK and the line joining the focus S with P and the tangent RZ on P",null,null,null,null,null,null,null,"FIND QV",{"$f":"yp-Q_Y+DYDX*Q_X-TAN(PHI)*xp","v":-8.8883849829139905},"XLYSH",{"$f":"M8/(DYDX-TAN(PHI))","v":6.2837801620302223},"YLYSH",{"$f":"Q_Y+DYDX*(O8-Q_X)","v":4.5330763412861366},null,null,null,null,null,null,null,null,null,null,null,null,0,0,null,"a",{"$f":"-1/2*g/(varxiki*COS(firipsi))^2","v":-1.1778510282469032E-2},null,"ymax",{"$f":"(varxiki*SIN(firipsi))^2/(2*g)","v":89.22490497485947},null,null,null,null,null,"TaNTd = (Yt - YD) / (Xt - XD): TanVE = (Yv - YE) / (Xv - XE)",null,null,null,null,null,null,null,null,null,null,null,0,-4.5000000000000018,-1.8000000000000007,4.0500000000000034,39.183063943494815,4.2500000000000036,0.22222222222222213,-0.42352941176470571,0.65882352941176492,0.97618706018395263,0.21693045781865605,-0.27052504151502987,-10.43722014033157,-10.276940024315369,-90.042432110328832,36.450000000000031,12.550000000000008,-2.8902652413026093,-0.56745462779687594,0.51307544245059922,0.6134256055363323,null,null,-185.62722918919664]
[null,null,"xekino",null,null,null,null,null,null,null,null,"QV",{"$f":"Q_X","v":3.1369662545765573},{"$f":"Q_Y","v":6.7141433823551884},null,null,null,null,"TAN1",{"$f":"TSP","v":0.35887485844697714},"X1",{"$f":"CC","v":7.0710678118654746},0,"Y1",null,null,null,null,null,null,null,null,"b",{"$f":"(g/(varxiki*COS(firipsi))^2)*xxekina+TAN(firipsi)","v":0},null,null,null,null,"focus",null,null,null,"srq_",{"$f":"y_r-Y_Q+X_Q*TANF_Q-x_r*tanf_r","v":35.689961989943782},"x_v",{"$f":"srq_/(TANF_Q-tanf_r)","v":43.517893867931235},{"$f":"y_r+tanf_r*(AT9-x_r)","v":70.487674930138965},"y_v",null,null,null,null,null,null,0,-4.4000000000000021,-1.7600000000000009,3.8720000000000034,36.747402968917449,4.0720000000000027,0.22727272727272715,-0.43222003929273078,0.64390962671905738,0.97513285579145981,0.22162110358896803,-0.2787679991607796,-10.571352602275805,-10.90916593534199,-89.640279435743835,34.073600000000042,12.016000000000009,-2.8274333882308134,-0.55470380588781953,0.46918682556853808,0.60143376974768548,null,null,-180.88688766043788]
[null,null,3,9,null,null,null,null,null,"PF",{"$f":"SQRT((xp-F_X)^2+(yp-F_Y)^2)","v":8.1378845877115964},null,{"$f":"V_X","v":6.2837801620302223},{"$f":"V_Y","v":4.5330763412861366},"X_X",null,"X_Y",null,"TAN2",{"$f":"TAN(PSI)","v":-0.69310328008367272},"X2",{"$f":"xp","v":7},{"$f":"yp","v":5.0497524691810387},"Y2",null,"IY",null,null,null,null,null,null,"c",{"$f":"-1/2*g*xxekina^2/(varxiki*COS(firipsi))^2-TAN(firipsi)*xxekina","v":89.22490497485947},null,"focus",{"$f":"c_+1/(4*a)","v":67.999809949718937},null,{"$f":"0","v":0},{"$f":"c_+1/(4*a)","v":67.999809949718937},null,null,null,null,"rvq",{"$f":"x_r","v":60.925051415103709},{"$f":"y_r","v":45.504701537178335},null,"TP",null,null,null,null,null,0,-4.3000000000000025,-1.7200000000000011,3.698000000000004,34.417375493201156,3.8980000000000041,0.23255813953488358,-0.44125192406362218,0.62801436634171404,0.97400802703919653,0.22651349466027812,-0.28752918716753623,-10.706745378162054,-11.583912347695474,-89.149315889034057,31.802800000000051,11.49400000000001,-2.7646015351590174,-0.5392223557577045,0.42618544357858823,0.5891053048214332,null,null,-176.01064411147388]
[null,null,3,0,null,null,null,null,null,"PF∙CD",{"$f":"PF*BBT","v":70.710678118654769},"QX",{"$f":"yp-Q_Y+DYDX*Q_X-TSP*xp","v":-6.3507565228617935},"XLYSH",{"$f":"M11/(DYDX-TSP)","v":6.0369662545765586},"YLYSH",{"$f":"Q_Y+DYDX*(O11-Q_X)","v":4.7041438701125387},null,null,null,"SSAA",{"$f":"yp-0+CC*TAN(PSI)-xp*TSP","v":-2.3633518340458401},"XLYSH",{"$f":"V11/(TAN(PSI)-TSP)","v":2.246578847490929},"YLYSH",{"$f":"0+TAN(PSI)*(X11-CC)","v":3.3438691259354787},null,null,null,null,null,null,null,null,null,null,null,null,0,{"$f":"AN10","v":67.999809949718937},null,null,null,null,"ves",{"$f":"IF(vimata2>3,x_v,1000)","v":1000},{"$f":"IF(vimata2>3,y_v,1000)","v":1000},"TP",{"$f":"IF(vimata2>2,TX_,1000)","v":-26.110736320758733},{"$f":"IF(vimata2>2,TY_,1000)","v":113.31562931807156},null,null,null,null,0,-4.2000000000000028,-1.6800000000000013,3.5280000000000054,32.190583825709098,3.7280000000000055,0.23809523809523794,-0.450643776824034,0.6110515021459233,0.97280621468536688,0.23162052730603958,-0.29685699556551942,-10.843214639559431,-12.303819979024265,-88.563306750197469,29.635200000000065,10.984000000000016,-2.7017696820872215,-0.52107137561739325,0.38424100329000127,0.57646375186501908,null,null,-170.99829320736009]
[null,null,null,"Draw HI parallel to DK. Since DK conjugate to PG, RZ parallel to DK. It Is well known from optics that the RZ makes equal angle IPR = HPZ (so SP reflected to PH) perpendicular PF to DK is  DFꞱHI so PH=PI. From Thales Since CH=CS then CH/CS=EI/SE so SE=EI",null,null,null,null,null,"AA∙BB",{"$f":"AA*BB","v":70.710678118654755},null,{"$f":"Q_X","v":3.1369662545765573},{"$f":"Q_Y","v":6.7141433823551884},null,null,null,null,null,null,null,null,null,"IX",null,"IY",null,"parabola","firipsi",{"$f":"RADIANS(AE12)","v":1.1170107212763709},64,null,null,{"$f":"1/(4*AH8)","v":-21.225095025140529},null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(vimata2>3,x_v+(XE_-x_v)*20,1000)","v":1000},{"$f":"y_v+(YE_-y_v)*20","v":-706.08152769279138},null,{"$f":"IF(vimata2>2,p_X,1000)","v":-78.332208962276212},{"$f":"IF(vimata2>2,P_y,1000)","v":16.952731945223299},null,null,null,null,0,-4.1000000000000032,-1.6400000000000015,3.3620000000000054,30.064630490993967,3.5620000000000052,0.24390243902439004,-0.46041549691184702,0.59292532285233079,0.9715203387831296,0.23695618019100703,-0.30680569989919271,-10.980545279796624,-13.071593087777941,-87.875820428341953,27.568400000000064,10.486000000000015,-2.6389378290154255,-0.500322499093105,0.34351904024600427,0.56354286827612377,null,null,-165.85033392920531]
[null,null,"parper","Since EI=SE then PE=EI/2+(HP+PH)/=2a/2=a",null,null,null,null,null,null,null,null,{"$f":"X_X","v":6.0369662545765586},{"$f":"X_Y","v":4.7041438701125387},"A",null,"HS",null,"HI",null,null,null,null,null,null,null,null,"varxiki",47,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"TQ",null,null,null,null,null,0,-4.0000000000000036,-1.6000000000000014,3.200000000000006,28.037118254200166,3.4000000000000057,0.24999999999999978,-0.47058823529411725,0.57352941176470662,0.97014250014533188,0.24253562503633275,-0.31743633276814121,-11.118487080317283,-13.889972466874404,-87.080268694867684,25.600000000000069,10.000000000000018,-2.5761059759436296,-0.47705761252122153,0.30418026543063659,0.55038927335640186,null,null,-160.56808171706865]
[null,null,12,0,null,null,null,null,null,null,null,"FP",{"$f":"xp","v":7},{"$f":"yp","v":5.0497524691810387},{"$f":"AA","v":10},0,{"$f":"CC","v":7.0710678118654746},0,{"$f":"CC","v":7.0710678118654746},{"$f":"0","v":0},null,"2ax-x^2=t^2*x^2 so 2a=(t^2+1)*x x=2a/(t^2+a) y-sqrt(4a^2/(1+t^2)-4a^2/(1+t^2)^2)",null,null,null,null,null,"g",{"$f":"10","v":10},null,-60,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(vimata2>2,TX_,1000)","v":-26.110736320758733},{"$f":"IF(vimata2>2,TY_,1000)","v":113.31562931807156},null,null,null,null,0,-3.9000000000000035,-1.5600000000000014,3.0420000000000056,26.105650150111252,3.2420000000000053,0.25641025641025617,-0.48118445404071525,0.55274521900061768,0.96866386604404509,0.24837535026770363,-0.32881770615329542,-11.256750497221276,-14.761699878458904,-86.169959170667525,23.72760000000007,9.5260000000000176,-2.5132741228718336,-0.45136853178032615,0.26637993101591778,0.53706575593850203,null,null,-155.15379132133504]
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[48.215628780035537,0.66348468745850187,31.183780310549576,null,null,null,null,null,null,null,{"$f":"Q_X","v":3.1369662545765573},{"$f":"Q_Y","v":6.7141433823551884},{"$f":"xp","v":7},null,-0.28797932657906444,18.94147294778266,-5.6107199015924003,-6.1030181256036053,19.699545734685657,6.1030181256036053,null,-1.806415775814131,7.8968327206898135,-10.017084552036437,20.603443899086642,520.94015272330444,1.9009494079227376,-47.869683254724364,62.234371219964473,145.3405924550481,42.450190050281087,-1.806415775814131,-14.354702016747577,-12.607005253110522,1.1276671128686131,-0.88678652466520247,0.74818986193886272,-0.66348468745850175,31.053382675655655,-10.000000000000002,null,null,null,"cx_",{"$f":"CE60+SIGN(0-CE60)*1/CH60*40*KK*COS(ATAN(CI62))","v":42.712601970332699},null,null,null,null,null,null,null,null,null,0,{"$f":"BD35+deltt","v":-1.7000000000000015},-0.6800000000000006,0.57800000000000107,3.0689117028679789,0.77800000000000102,0.58823529411764652,-0.87403598971722329,-0.8637532133676068,0.86193421515776969,0.50702012656339346,-1.191301788377741,-12.947319205677914,-45.851497432635689,-31.464651003672355,1.9652000000000052,2.134000000000003,-1.1309733552923227,{"$f":"kenxky+rhoky*COS($BT36)","v":0.44695899671000139},{"$f":"kenyky+rhoky*SIN($BT36)","v":3.5728624382607821E-2},null,null,null,{"$f":"$BP36*$BH36^m","v":-27.753177772015533},null,null,null,null,{"$f":"\"Angle of initial speed = \"&TEXT(AE12,\"0,00\")","v":"Angle of initial speed = 064"},null,null,null,null,null,null,"TanpRpp = -1 / tanFP"]
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[43.531321268855422,0.69827082539770169,32.818728793691953,"COS(φ)*COS(ψ)/a²+SIN(φ)*SIN(ψ)/b² so tanψ=-(b/a)²/tan²φ",null,null,null,null,null,null,{"$f":"xp","v":7},{"$f":"yp","v":5.0497524691810387},null,null,-0.4450589592585541,16.784805635316616,-8.0059416091402245,-9.8273386291835099,18.259743860256634,9.8273386291835099,null,-1.6493361431346414,9.4934581609424615,-10.269965178798769,20.603443899086642,477.42225885537334,2.1121660088030416,-43.517893867931249,66.918678731144595,124.68320223478358,42.45019005028113,-1.6493361431346414,-6.3283186757816097,-13.878259486399593,1.0251519207896485,-0.97546517713172254,0.7158336778878267,-0.69827082539770124,29.506379401361812,-10.000000000000002,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0,-1.5000000000000013,-0.60000000000000053,0.45000000000000084,2.3436083290515972,0.6500000000000008,0.66666666666666607,-0.9230769230769228,-1.230769230769228,0.83205029433784383,0.5547001962252287,-1.4507543593582892,-12.725475089872907,-47.628740077345832,-24.959686617468186,1.3500000000000032,1.7500000000000022,-1.0053096491487308,0.52701973456936602,7.9742387478779597E-2,null,null,null,-20.123142682678662,null,null,null,120,null,-60,100,null,null,null,null,"PerPrxP2 = XP + Sgn(0 - XP) * 1 / VELOCITY1 * KK * Cos(Atn(TanpRpp)):"]
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[-0.31415926535897931,9.5105651629515346,-2.1850801222441052,-189.06175978026494,51.292385023511279,9.7583515441581454,8.39916621005883,2.3663144634725159,"X5Y5",{"$f":"J11","v":-2.5215924547815809},{"$f":"K11","v":-7.3525181714080743},{"$f":"J9","v":-1.4451326206513047},null,{"$f":"N13","v":0.80901699437494745},{"$f":"-O13","v":-0.58778525229247314},{"$f":"N14*COS(M13)+O14*SIN(M13)","v":0.85810603722368894},{"$f":"-N14*SIN(M13)+O14*COS(M13)","v":-0.5134725200828737},null,null,null,null,null,"Xt ",{"$f":" Spq / (TANFP - TANFQ)","v":11.174479348787822},{"$f":"xd_-Xt","v":-12.458838913764056},"S",-1.2166610051582139E-14,1.2434497875801753E-14,null,"TO VT","STV","SSAA","TT_X","TT_Y","PERPENDICULAF FROM D TO VT"]
[-0.37699111843077515,9.2977648588825144,-2.6030336752460026,-189.06175978026479,51.758045495812539,9.6552688044163375,8.8648266823600892,2.4310253916622768,null,"Q",null,null,null,null,null,null,null,null,{"$f":"P11","v":0.78380667756015621},{"$f":"Q11","v":-1.7591334874286595},"SRQ  ",{"$f":" RY_ - QY_ + QX_ * TANFQ - RX_ * TANFR","v":-48.603311124163248},"Yv  ",{"$f":"QY_ + TANFQ * (Xv - QX_)","v":10.541986098517512}," = YQ + taNFq * (Xv - XQ)",null,{"$f":"$AO$25","v":11.174479348787822},{"$f":"$AP$25","v":-6.1290705365297633},null,"TANPERVT",{"$f":"-1/AE16","v":0.17865672032464955},{"$f":"v_3y-S_3Y+AE15*S_3X-AE16*v_3x","v":55.154845369648825},{"$f":"IF(VIMATA>3,AF15/(AE15-AE16),100)","v":9.5489967686194088},{"$f":"IF(VIMATA>3,S_3Y+AE15*(AG15-S_3X),100)","v":2.9692862295333065},"TANPER",{"$f":"t_3y-D_3Y+D_3X*AE15-t_3x*AE16","v":58.132559072931166},{"$f":"IF(VIMATA>3,AJ15/(AE15-AE16),100)","v":10.064530414665381},{"$f":"IF(VIMATA>3,D_3Y+AE15*(AK15-D_3X),100)","v":8.367607667053889E-2},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"-(TANFP*XP_*velocity1-YP_*velocity1+TANFQ*QX_*velocity2+QY_*velocity2)*(velocity1-velocity3)","v":-126.18618526517011}]
[-0.43982297150257099,9.0482705246601967,-3.0107142435446703,-189.06175978026468,52.314885208709157,9.5360159261463728,9.4216663952567075,2.5062144621263238,"FI2",{"$f":"AD8","v":0.12566370614359174},1,"energy_3"," velocity2","TAN",null,"perp2",null,null,{"$f":"P10","v":1.2533323356430448},{"$f":"Q10","v":-7.0153103301433344},null,null,"Xv ",{"$f":" SRQ / (TANFQ - TANFR)","v":8.1960830460237872},"PerPrYq2 = YQ + taNprpQ * (PerPrxQ2 - XQ)",null,null,null,null,"TANVT",{"$f":"(v_3y-t_3y)/(v_3x-t_3x)","v":-5.5973265275598392},null,{"$f":"IF(VIMATA>3,S_3X,100)","v":-7.0710678118654577},{"$f":"IF(VIMATA>3,S_3Y,100)","v":7.9936057773011271E-15},"TANPER","SSAA",{"$f":"IF(VIMATA>3,D_3X,100)","v":-1.2843595649762343},{"$f":"IF(VIMATA>3,D_3Y,100)","v":-1.9438793864175108},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"((TANFP*XP_+YP_)*velocity1-(TANFQ*QX_+QY_)*velocity2)*(velocity1-velocity3)","v":-127.76589447514189}]
[-0.50265482457436683,8.7630668004386365,-3.4065128981885686,-189.06175978026471,52.966283079701263,9.4018971423045734,10.073064266248814,2.5914042867717897,"X1Y1",{"$f":"AA*COS(J16)","v":9.921147013144779},{"$f":"BB*SIN(J16)","v":0.88623979361356953},{"$f":"$AQ$35","v":7.523985435200423},{"$f":"$AO$32","v":1.7348181962615474},{"$f":"BB*COS(J16)/(AA*(-SIN(J16)))","v":-5.5973265275598401},{"$f":"ATAN(N19)","v":0.17679151088759476},{"$f":"J17","v":9.921147013144779},{"$f":"K17","v":0.88623979361356953},null,{"$f":"M17*COS(N18)","v":0.30510595546671043},{"$f":"M17*SIN(N18)","v":-1.7077776582503106},"TaNTd ",{"$f":" (Yt - yd_) / (Xt - xd_)","v":-0.33592144332876889},"TanVE",{"$f":" (Yv - YE) / (Xv - XE)","v":0.69050120724195052},null,null,null,null,null,"TO RV",null,"SSAA",null,null,"PERPENDICULAF FROM E TO VT",null,null,null,null,null,null,null,null,null,null,{"$f":"epilogi","v":1},null,null,null,null,null,null,null,null,null,{"$f":"-((TANFP*XP_+YP_)*velocity1-(TANFR*RX_+RY_)*velocity3)*(velocity1-velocity2)","v":111.62524107227878},null,null,{"$f":"epilogi","v":1}]
[-0.56548667764616267,8.4432792550201512,-3.788867602711024,-189.06175978026462,53.716234220600334,9.2544304140842097,10.823015407147885,2.6861391633281504,"X2Y2",{"$f":"J17+SIGN(K17)*M17*COS(N18)","v":10.22625296861149},{"$f":"K17+(N17)*(J18-J17)","v":-0.82153786463674461},"SIGNX",{"$f":"SIGN(J18-J17)","v":1},{"$f":"ATAN(N17)","v":-1.394004815907302},null,{"$f":"IF(VIMATA>1,Bx,QX_)","v":-1.4277429664968366},{"$f":"Q17+TAN(O17)*(P18-P17)","v":-1.1413156694744802},{"$f":"(P18-P17)*(J18-J17)+(Q18-Q17)*(K18-K17)","v":0},{"$f":"1/M17*1*COS(O17)*ddd_2","v":17.023334969462422},{"$f":"1/M17*1*SIN(O17)*ddd_2","v":3.0413331946320734},"Stv ",{"$f":" Yv - Yt + Xt * TaNTd - Xv * TanVE","v":7.257904165820241},"Ys ",{"$f":" Yt + TaNTd * (Xs - Xt)","v":7.9936057773011271E-15},null,null,{"$f":"(D_3Y-t_3y)/(D_3X-t_3x)","v":-0.33592144332876889},{"$f":"(v_3y-E_3Y)/(v_3x-E_3X)","v":0.69050120724195052},null,"TANPERRV",{"$f":"-1/AE19","v":-3.0053567999888298},{"$f":"r_3y-S_3Y+AE18*S_3X-AE19*r_3x","v":29.065909761518654},{"$f":"AF18/(AE18-AE19)","v":-8.7073319077290847},{"$f":"S_3Y+AE18*(AG18-S_3X)","v":4.9175574270813334},"TANPER",{"$f":"t_3y-E_3Y+E_3X*AE15-t_3x*AE16","v":52.676449242687973},{"$f":"IF(VIMATA>3,AJ18/(AE15-AE16),100)","v":9.1199103221051132},{"$f":"IF(VIMATA>3,E_3Y+AE15*(AK18-E_3X),100)","v":5.3710231792241512},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"BD17+BD16","v":-16.140653402863109},null,null,{"$f":"CC","v":7.0710678118654746}]
[-0.62831853071795851,8.0901699437494745,-4.1562693777745334,-189.06175978026474,54.569393710160206,9.095351827135314,11.676174896707757,2.79000297451547,"X3Y3",{"$f":"J18+P20","v":10.662592995645891},{"$f":"K18+Q20","v":7.8243987151575656E-2},"SIGNY",{"$f":"SIGN(K18-K17)","v":-1},{"$f":"-1/N17","v":0.17865672032464952},{"$f":"TAN(O17)","v":0.17865672032464952},"x","y",null,{"$f":"S18*S17","v":5.1939208810876965},{"$f":"T18*T17","v":-5.1939208810876982},null,null,"X_S",{"$f":" Stv / (TaNTd - TanVE)","v":-7.0710678118654577},null,null,null,null,null,"TANRV",{"$f":"(v_3y-r_3y)/(v_3x-r_3x)","v":0.33273919422935633},null,{"$f":"S_3X","v":-7.0710678118654577},{"$f":"S_3Y","v":7.9936057773011271E-15},"TANPER","SSAA",{"$f":"IF(VIMATA>3,E_3X,100)","v":-2.2289796575365006},{"$f":"IF(VIMATA>3,E_3Y,100)","v":3.3434677161361011},null,null,"use the macro to find  A, B, C, D, E, T,V, S",null,null,null,null,{"$f":"IF(epilogi=1,STATHERA,IF(epilogi=2,STATH22,STATH2))","v":171.57287525380994},null,"energia",{"$f":"IF(graviminus=TRUE, ENERGY, IF(gravpluc=TRUE,ENERGY22,energy_3))","v":-42.893218813452449},null,null,null,null,null,null,{"$f":"BD18/BD15","v":0.12791141414525548}]
[-0.69115038378975435,7.7051324277578939,-4.5072682564228277,-189.06175978026468,55.531127861716733,8.9266193413096282,12.637909048264284,2.9026320295281756,"X4Y4",{"$f":"J18+P21","v":9.5053460589037417},{"$f":"K18+Q21","v":-0.12850595517252361},"F",{"$f":"-N18","v":1.394004815907302},{"$f":"-M18*DAA*COS(PI()/5)","v":-0.80901699437494745},{"$f":"-M19*DAA*SIN(PI()/5)","v":0.58778525229247314},{"$f":"N20*COS(M20)+O20*SIN(M20)","v":0.43634002703440028},{"$f":"-N20*SIN(M20)+O20*COS(M20)","v":0.89978185178832026},null,null,null,null,null,null,{"$f":"SRQ-KK/velocity2*(1+TANFQ^2)^0.5 +KK/velocity3*(1+TANFR^2)^0.5","v":-110.42461811004911},null,null," (Yt - yd_) / (Xt - xd_)"," (Yv - YE) / (Xv - XE)",null,null,null,null,null,null,"PERPENDICULAF FROM E TO RV",null,null,null,null,"AX",{"$f":"ax","v":0.78380667756015621},{"$f":"Ay","v":-1.7591334874286577},null,null,null,null,null,"maza",{"$f":"IF(graviminus=TRUE, MASS, IF(gravpluc=TRUE,MASS,mass_2))","v":5}]
[-0.75398223686155019,7.2896862742141169,-4.8404790064380157,-189.06175978026468,56.607573605898189,8.7504150180567351,13.714354792445739,3.023723399215581,"X5Y5",{"$f":"J18","v":10.22625296861149},{"$f":"K18","v":-0.82153786463674461},{"$f":"J16","v":0.12566370614359174},null,{"$f":"N20","v":-0.80901699437494745},{"$f":"-O20","v":-0.58778525229247314},{"$f":"N21*COS(M20)+O21*SIN(M20)","v":-0.72090690970774851},{"$f":"-N21*SIN(M20)+O21*COS(M20)","v":0.693031909464221},null,null,null,{"$f":"Spq-KK/velocity2*(1+TANFQ^2)^0.5+SIGN(YP_)*KK/velocity1*(1+TANFP^2)^0.5","v":-7.3037095977648052},null,null,null,null,null,null,null,null,null,null,null,null,null,"TANPER",{"$f":"r_3y-E_3Y+E_3X*AE18-r_3x*AE19","v":11.170239484624663},{"$f":"IF(VIMATA>3,AJ21/(AE18-AE19),100)","v":-3.3462906710808475},{"$f":"IF(VIMATA>3,E_3Y+AE18*(AK21-E_3X),100)","v":6.7013859683940158},null,"BX",{"$f":"Bx","v":-1.4277429664968366},{"$f":"YB","v":-1.1413156694744784},null,null,null,null,null,"STATHERI",{"$f":"IF(epilogi=1,STATHERA,IF(epilogi = 2,STATH22,STATH2))","v":171.57287525380994}]
[-0.81681408993334603,6.8454710592868881,-5.1545865972192981,-189.06175978026471,57.805706668692814,8.5691444737364062,14.912487855240364,3.1530395763707508,null,"R",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"LINE AD","ay","LINE CE",null,"LINE EBD",null,null,null,null,"TANPER","SSAA",{"$f":"IF(VIMATA>3,E_3X,100)","v":-2.2289796575365006},{"$f":"IF(VIMATA>3,E_3Y,100)","v":3.3434677161361011},null,"CX",{"$f":"Cx","v":-3.1404819021063783},{"$f":"CY","v":3.0401751937396675},null,null,null,null,null,"pot_energy",{"$f":"IF(elasti,1/2*mass_2*STATH2*((AA*COS(gon_1))^2+(BB*SIN(gon_1))^2),IF(graviminus,STATHERA*MASS/SQRT((AA*COS(gon_1)+CC)^2+(BB*SIN(gon_1))^2),STATH22*MASS/SQRT((AA*COS(gon_1)-CC)^2+(BB*SIN(gon_1))^2)))","v":54.569393710160206}]
[-0.87964594300514187,6.3742398974868983,-5.4483513896079705,-189.06175978026465,59.133419269974951,8.3854318395272216,16.240200456522501,3.2904103550086781,"FI3",{"$f":"AD9","v":2.0106192982974678},20,"energy_3","velocity3","TAN",null,"perp3",null,null,null,null,null,"SSAA = y2 - y1 + TAN1 * x1 - TAN2 * x2",null,null,null,{"$f":"IF(VIMATA>2,ax,100)","v":0.78380667756015621},{"$f":"IF(VIMATA>2,Ay,100)","v":-1.7591334874286577},{"$f":"IF(VIMATA>2,Cx,100)","v":-3.1404819021063783},{"$f":"IF(VIMATA>2,CY,100)","v":3.0401751937396675},{"$f":"IF(VIMATA>2,E_3X,100)","v":-2.2289796575365006},{"$f":"IF(VIMATA>2,E_3Y,100)","v":3.3434677161361011},null,null,null,null,null,{"$f":"XD","v":-7.141428428542846},null,null,"XD",{"$f":"xd_","v":-1.2843595649762343},{"$f":"yd_","v":-1.9438793864175108},null,null,{"$f":"energy_3-mass_2*STATH2*(AO29^1+AP29^2)","v":138.87381315255334},null,null,"kin_energ",{"$f":"IF(elasti,energy_3-pot_energy,IF(gravpluc,ENERGY22+pot_energy,ENERGY+pot_energy))","v":11.676174896707757},null,null,null,"sinf","cos","duajrubitsa",null,"right side"]
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[-1.822123739082081,-2.4868988716485569,-6.848917213771573,-189.06175978026445,104.09084443348333,7.2864485861703185,61.197625620030877,6.387363859998942,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"-SRQ-KK/v2_x+KK/v3_x","v":-13.217995861722654},{"$f":"SCB","v":-13.217995861722624},null,null,null,null,{"$f":"AB37","v":-7.0710678118654577},{"$f":"AC37","v":7.9936057773011271E-15}]
[-1.884955592153877,-3.0901699437494838,-6.7249851196395705,-189.06175978026451,109.77263870751186,7.4009847412777665,66.87941989405941,6.6772958545636527,null,null,null,{"$f":"TanVE","v":0.69050120724195052},null,null,null,null,null,null,null,null,null,"SSAA = y2 - y1 + TAN1 * x1 - TAN2 * x2",null,null,null,null,null,{"$f":"CC","v":7.0710678118654746},null,null,"SSAA","RTT_X","RTT_Y"]
[-1.9477874452256729,-3.6812455268467903,-6.5745125815938064,-189.06175978026445,115.97516314197641,7.5349707573729017,73.08194432852396,6.9800641987746772,null,null,null,{"$f":"(-TANFQ*v2_x+TANFR*v3_x)/(v3_x-v2_x)","v":0.69050120724195096},null,null,null,null,null,null,null,null,null,null,null,null,null,"find the perpendicular from S to RV",null,null,"TANRRX",{"$f":"(r_3y-v_3y)/(r_3x-v_3x)","v":0.33273919422935633},{"$f":"S_3Y-r_3y+r_3x*AD40-S_3X*AD41","v":-29.06590976151865},{"$f":"IF(VIMATA>3,AE40/(AD40-AD41),100)","v":-8.7073319077290829},{"$f":"IF(VIMATA>3,r_3y+AD40*(AF40-r_3x),100)","v":4.9175574270813298}]
[-2.0106192982974687,-4.2577929156507359,-6.3980934459975813,-189.06175978026448,{"$f":"IF(elasti,1/2*mass_2*STATH2*((AA*COS($A41))^2+(BB*SIN($A41))^2),IF(graviminus,STATHERA*MASS/SQRT((AA*COS($A41)+CC)^2+(BB*SIN($A41))^2),STATH22*MASS/SQRT((AA*COS($A41)-CC)^2+(BB*SIN($A41))^2)))","v":122.73992023816223},7.6853367041583018,{"$f":"IF(elasti,energy_3-E41,IF(gravpluc,ENERGY22+E41,ENERGY+E41))","v":79.846701424709778},{"$f":"SQRT(2*G41/mass_2)","v":7.2959669875308411},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"KATH FROM S",{"$f":"-1/AD40","v":-3.0053567999888298},"LINE SR'",{"$f":"IF(VIMATA>3,S_3X,100)","v":-7.0710678118654577},{"$f":"IF(VIMATA>3,S_3Y,100)","v":7.9936057773011271E-15}]
[-2.0734511513692646,{"$f":"AA*COS(A42)","v":-4.8175367410171619},{"$f":"BB*SIN(A42)","v":-6.1964239585808576},{"$f":"IF(elasti,mass_2*$H42*AA*BB/SQRT((AA*SIN($A42))^2+(BB*COS($A42))^2),IF(graviminus,MASS*(-AA*BB-BB*CC*COS(A42))/SQRT((AA*SIN(A42))^2+(BB*COS(A42))^2)*$H42,MASS*(-AA*BB+BB*CC*COS($A42))/SQRT((AA*SIN($A42))^2+(BB*COS($A42))^2)*$H42))","v":-189.06175978026454},130.10784172662889,7.848842597830914,87.214622913176441,7.6251611092564877,null,null,null,null,null,null,null,null,null,null,null,null,null,"point at which the lines VE and TD meet",null,null,null,null,null,null,null,null,"LINE R'R",{"$f":"RTT_X","v":-8.7073319077290829},{"$f":"RTT_Y","v":4.9175574270813298}]
[-2.1362830044410606,-5.3582679497899752,-5.9703000166764451,-189.06175978026445,138.11722587711861,8.0221890847120552,95.224007063666164,7.9676013564797179,null,null,null,null,null,"tanve",null,null,null,null,null,null,null,null,null,null," ",null,null,null,null,null,null,{"$f":"r_3x","v":-4.257792915650727},{"$f":"r_3y","v":6.398093445997584}]
[-2.1991148575128565,-5.8778525229247416,-5.7206140281768381,-189.06175978026445,146.8008078617338,8.2021079693348575,103.90758904828135,8.3229637769359286,null,null,null,null,null,null,{"$f":"SIGN(QY_)*velocity3*COS(ATAN(TANFR))-SIGN(RY_)*velocity2*COS(ATAN(TANFQ))","v":5.057267966465707},null,null," ",null,null,null,null,null,null," "]
[-2.2619467105846525,-6.3742398974869072,-5.4483513896079661,-189.06175978026445,156.18173548565872,8.3854318395272252,113.28851667220627,8.6905510631645697,null,null,null,null,null,null,{"$f":"O43/O44","v":0},null,null,null,null,null,null,null,null,null," "]
[-2.3247785636564484,-6.845471059286897,-5.1545865972192928,-189.0617597802644,166.26822089482499,8.5691444737364098,123.37500208137254,9.0691786501083822,null,null,null,null,null,"stathera=1/2*(v1^2-v2^2)/(1/",null,null,null,null,null,null,null,null,null,null,"Determinant "]
[-2.3876104167282444,-7.2896862742141257,-4.8404790064380094,-189.0617597802644,177.04668414396528,8.7504150180567386,134.15346533051283,9.4570420086660931,null,null,null,null,null,"stathera",{"$f":"1/2*(v_o^2-vo^2)/(1/(AA-CC)-1/(AA+CC))","v":-171.57287525380994}]
[-2.4504422698000403,-7.7051324277579027,-4.5072682564228206,-189.06175978026437,188.47333124759029,8.9266193413096317,145.58011243413785,9.8515688237673711,null,null,null,null,null,null,{"$f":"v_o","v":1.7157287525380993}]
[-2.5132741228718363,-8.0901699437494852,-4.1562693777745254,-189.0617597802644,200.46436145687807,9.0953518271353193,157.57114264342562,10.249264775043642,null,null,null,null,null,{"$f":"10","v":10},{"$f":"vo*(AA-CC)/(AA+CC)","v":1.7157287525380993},"v_`",null,null,null,null,{"$f":"SIGN(YP_)*(-TANFQ+TANFR)*v1_x*v3_x","v":-120.03970081998155},{"$f":"(TANFQ*SIGN(YP_)+TANFQ)*v2_x*v1_x","v":0},{"$f":"(TANFP-TANFR)*v3_x+v1_x","v":2.4696648815077564},{"$f":"-TANFP*v1_x^2-TANFQ*SIGN(YP_)*v2_x^2","v":-1.7939873736610008},{"$f":"SUM(U49:X49)","v":-119.36402331213479}]
[-2.5761059759436322,-8.4432792550201601,-3.7888676027110137,-189.06175978026442,212.88542070606346,9.2544304140842115,169.99220189261101,10.64556877743383,null,null,null,null,null,null,null,"V1X",{"$f":"velocity1*COS(ATAN(TANFP))","v":3.7749247904246257},"v1_x",{"$f":"ABS(SIGN(YP_)*velocity1*COS(ATAN(TANFP)))","v":3.7749247904246257},"v1_y",{"$f":"velocity1*SIN(ATAN(TANFP))","v":0.33720784126473996},"v12x",{"$f":"V1X+V2X","v":4.0800307458913361},"v1xp",{"$f":"V1X*YP_-v1_y*XP_","v":-26.904902369069521},"v12y",{"$f":"v1_y+v2_y","v":-1.3705698169855707},"sx",{"$f":"(v2xq+v1xp)*v13x-(v3xr+v1xp)*v12x","v":-149.758206798294},{"$f":"AC50/Determinant","v":-7.0710678118654515}]
[-2.6389378290154282,-8.7630668004386454,-3.406512898188558,-189.06175978026442,225.54153431594767,9.4018971423045787,182.64831550249522,11.034742573722784,null,null,null,null,null,null,null,"V2X",{"$f":"velocity2*COS(ATAN(TANFQ))","v":0.30510595546671043},"v2_x",{"$f":"SIGN(QY_)*velocity2*COS(ATAN(TANFQ))","v":0.30510595546671043},"v2_y",{"$f":"velocity2*SIN(ATAN(TANFQ))","v":-1.7077776582503106},"v13x",{"$f":"V1X+V3X","v":9.1372987123570439},"v2xq",{"$f":"V2X*QY_-v2_y*QX_","v":17.213510252268545},"v13y",{"$f":"v1_y+v3_y","v":2.1214798192050477},"YS",{"$f":"v12y*(v3xr+v1xp)-v13y*(v2xq+v1xp)","v":-8.5265128291212022E-14}]
[-2.7017696820872241,-9.0482705246602038,-3.0107142435446579,-189.0617597802644,238.1695258906141,9.5360159261463764,195.27630707716165,11.40982930275943,null,null,null,null,null,null,null,"V3X",{"$f":"velocity3*COS(ATAN(TANFR))","v":5.3623739219324174},"v3_x",{"$f":"SIGN(RY_)*velocity3*COS(ATAN(TANFR))","v":5.3623739219324174},"v3_y",{"$f":"velocity3*SIN(ATAN(TANFR))","v":1.7842719779403076},"v23x",{"$f":"V2X+V3X","v":5.6674798773991277},"v3xr",{"$f":"V3X*RY_-v3_y*RX_","v":41.906030032172509},"v23y",{"$f":"v2_y+v3_y","v":7.6494319689996981E-2}]
[-2.7646015351590201,-9.2977648588825215,-2.6030336752459897,-189.06175978026437,250.43571074279336,9.6552688044163411,207.54249192934091,11.762723378802516,null,null,null,null,null,null,null,{"$f":"FI_1","v":-1.4451326206513047},{"$f":"TAN(P53)","v":-7.9158150883058118},{"$f":"-TANFP","v":-8.9328360162324941E-2},null,null,null,null,null,null,null,null,null,null,{"$f":"S_3X","v":-7.0710678118654577}]
[-2.827433388230816,-9.5105651629515418,-2.185080122244091,-189.06175978026445,261.94213083228493,9.758351544158149,219.04891201883248,12.084395227422636,null,null,null,null,{"$f":"-TANFQ*v2_x+TANFP*v3_x","v":2.1867897272737475},null,null,null,null,null,null,null,null,null,null,null,"Det=",{"$f":"-v12y*v13x+v12x*v13y","v":21.179008713082272}]
[-2.890265241302612,-9.6858316112863161,-1.7585030562678468,-189.06175978026442,272.2443155153789,9.8441691879557123,229.35109670192645,12.365303519712633,null,null,null,null,{"$f":"v3_x-v2_x","v":5.057267966465707},"tanve",null,null,null,{"$f":"(v1_x-SIGN(YP_)*v2_x)","v":4.0800307458913361},{"$f":"(v3_x-v1_x)","v":1.5874491315077917},{"$f":"S55*R55","v":6.4768412640902886}]
[-2.9530970943744079,-9.8228725072868901,-1.3249859821121404,-189.06175978026442,280.88204003539056,9.9118319269046484,237.98882122193811,12.595999926482961,null,null,null,null,{"$f":"M54/M55","v":0.4324053504331104},{"$f":"TanVE","v":0.69050120724195052},{"$f":"TanVE","v":0.69050120724195052},null,null,null,null,null,null,"Determinant "]
[-3.0159289474462039,-9.9211470131447808,-0.88623979361355276,-189.06175978026448,287.42163211569249,9.9606515363311345,244.52841330224004,12.767887147116134,null,null,null,null,null,null,null,null,null,{"$f":"-TANFQ*SIGN(YP_)*v2_x+TANFP*v1_x","v":-1.3705698169855696},{"$f":"TANFQ*v2_x-TANFR*v3_x","v":-3.4920496361906168}]
[-3.0787608005179998,-9.980267284282716,-0.44399602153402107,-189.06175978026448,291.50452072139996,9.9901385141979855,248.61130190794751,12.874038524823192,null,"tabve",null,null,null,null,null,null,null,{"$f":"R57*S55","v":-2.1757098656445355},{"$f":"-S57*R55","v":14.247669881836371},{"$f":"S58+R58","v":12.071960016191836},{"$f":"T58/T55","v":1.8638653510195939}]
[-3.1415926535897958,-10,1.7974798723779195E-14,-189.0617597802644,292.89321881345245,10,250,12.909944487358056]
[-3.2044245066615917,-9.9802672842827143,0.44399602153405687,-189.06175978026434,291.50452072139962,9.9901385141979855,248.61130190794717,12.874038524823183,null,null,null,null,{"$f":"-TANFQ*v2_x+TANFR*v3_x","v":3.4920496361906168},null,null,null,null,null,null,null,{"$f":"Stv","v":7.257904165820241},{"$f":"U60/U58","v":3.894006700564467},{"$f":"Stv","v":7.257904165820241}]
[-3.2672563597333877,-9.9211470131447754,0.88623979361358851,-189.06175978026437,287.42163211569198,9.9606515363311328,244.52841330223953,12.76788714711612,null,null,"TANVE",null,{"$f":"v3_x-v2_x","v":5.057267966465707},{"$f":"M60/M61","v":0.69050120724195096},null,null,null,null,null,null,{"$f":"TaNTd","v":-0.33592144332876889},{"$f":"TanVE","v":0.69050120724195052},{"$f":"U61-V61","v":-1.0264226505707195},{"$f":"W60/W61","v":-7.0710678118654577}]
[-3.3300882128051836,-9.8228725072868812,1.3249859821121757,-189.0617597802644,280.88204003538982,9.9118319269046449,237.98882122193737,12.595999926482941,null,null,{"$f":"TanVE","v":0.69050120724195052},null,{"$f":"SIGN(YP_)","v":-1},null,null,null,null,null,null,null,null,null,null,{"$f":"X_S","v":-7.0710678118654577}]
[-3.3929200658769796,-9.6858316112863037,1.7585030562678816,-189.06175978026445,272.24431551537816,9.8441691879557069,229.35109670192571,12.365303519712613,null,null,null,null,{"$f":"(-TANFQ*SIGN(YP_)*v2_x+SIGN(QY_)*TANFP*v1_x)/(v1_x-SIGN(YP_)*v2_x)","v":-0.3359214433287685}]
[-3.4557519189487755,-9.5105651629515258,2.1850801222441252,-189.06175978026448,261.94213083228408,9.7583515441581419,219.04891201883163,12.084395227422613,null,null,null,null,null,null,null,null,{"$f":"-TaNTd","v":0.33592144332876889}]
[-3.5185837720205715,-9.2977648588825019,2.603033675246023,-189.06175978026448,250.43571074279242,9.6552688044163304,207.54249192933997,11.762723378802489]
[-3.5814156250923674,-9.0482705246601807,3.0107142435446907,-189.06175978026445,238.16952589061313,9.536015926146364,195.27630707716068,11.409829302759402,null,null,null,null,null,null,{"$f":"TANFQ*SIGN(YP_)/v1_x+TANFP/v2_x","v":1.775543204939533},null,{"$f":"O66/O67","v":-0.50121815909705747}]
[-3.6442474781641634,-8.7630668004386205,3.406512898188589,-189.06175978026442,225.54153431594665,9.4018971423045681,182.6483155024942,11.034742573722754,null,null,null,null,null,null,{"$f":"-1/v2_x+SIGN(YP_)/v1_x","v":-3.5424558602149752}]
[-3.7070793312359593,-8.4432792550201334,3.7888676027110444,-189.06175978026448,212.88542070606249,9.2544304140842009,169.99220189261004,10.6455687774338]
[-3.7699111843077553,-8.090169943749455,4.1562693777745539,-189.06175978026442,200.46436145687713,9.0953518271353051,157.57114264342468,10.249264775043612]
[-3.8327430373795512,-7.7051324277578708,4.5072682564228481,-189.0617597802644,188.47333124758936,8.9266193413096175,145.58011243413691,9.8515688237673391,null,null,null,null,null,null,null,{"$f":"(SIGN(YP_)*TANFQ*v2_x +TANFP*v1_x)/(-v1_x+SIGN(YP_)*v2_x)","v":-0.50121815909705736}]
[-3.8955748904513472,-7.2896862742140911,4.8404790064380352,-189.06175978026442,177.0466841439644,8.7504150180567244,134.15346533051195,9.4570420086660629,null,null,null,null,null,null,null,{"$f":"-v1_x+SIGN(YP_)*v2_x","v":-4.0800307458913361}]
[-3.9584067435231431,-6.8454710592868597,5.1545865972193168,-189.06175978026448,166.26822089482417,8.5691444737363938,123.37500208137172,9.069178650108352,null,null,null,null,null,null,null,null,{"$f":"Spq","v":63.54540760653466}]
[-4.0212385965949391,-6.3742398974868681,5.4483513896079883,-189.06175978026442,{"$f":"IF(elasti,1/2*mass_2*STATH2*((AA*COS($A73))^2+(BB*SIN($A73))^2),IF(graviminus,STATHERA*MASS/SQRT((AA*COS($A73)+CC)^2+(BB*SIN($A73))^2),STATH22*MASS/SQRT((AA*COS($A73)-CC)^2+(BB*SIN($A73))^2)))","v":156.18173548565792},8.3854318395272109,{"$f":"IF(elasti,energy_3-E73,IF(gravpluc,ENERGY22+E73,ENERGY+E73))","v":113.28851667220547},{"$f":"SQRT(2*G73/mass_2)","v":8.6905510631645395},null,"tandt",null,null,{"$f":"(SAB-Spq)","v":-70.849117204299475},null,null,null,{"$f":"SAB","v":-7.3037095977648159}]
[-4.0840704496667346,{"$f":"AA*COS(A74)","v":-5.8778525229247034},{"$f":"BB*SIN(A74)","v":5.7206140281768576},{"$f":"IF(elasti,mass_2*$H74*AA*BB/SQRT((AA*SIN($A74))^2+(BB*COS($A74))^2),IF(graviminus,MASS*(-AA*BB-BB*CC*COS(A74))/SQRT((AA*SIN(A74))^2+(BB*COS(A74))^2)*$H74,MASS*(-AA*BB+BB*CC*COS($A74))/SQRT((AA*SIN($A74))^2+(BB*COS($A74))^2)*$H74))","v":-189.0617597802644},146.80080786173312,{"$f":"SQRT(B74^2+C74^2)","v":8.2021079693348433},103.90758904828067,8.3229637769359002,null,{"$f":"(SIGN(YP_)*TANFQ*v2_x-TANFP*v1_x)/(-v1_x+SIGN(YP_)*v2_x)","v":-0.3359214433287685},null,{"$f":"(Spq-KK/v2_x+SIGN(YP_)*KK/v1_x-Spq)/(TANFP-TANFQ)","v":-12.45883891376406},{"$f":"M73/(TANFP-TANFQ)","v":-12.458838913764055},{"$f":"O74/L74","v":-0.33592144332876855},{"$f":"(SIGN(YP_)*TANFQ*KK/v1_x-TANFP*KK/v2_x)/(TANFP-TANFQ)","v":4.1851911501122503},{"$f":"O74/P71","v":-1.025774414647932},{"$f":"Spq+(-SIGN(QY_)*KK/v2_x+SIGN(YP_)*KK/v1_x)","v":-7.3037095977648434}]
[{"$f":"A74-PI()/50","v":-4.1469023027385301},-5.3582679497899406,5.9703000166764619,-189.0617597802644,138.11722587711805,8.0221890847120445,95.224007063665596,7.9676013564796948,null,null,null,{"$f":"xd_-Xt","v":-12.458838913764056},null,null,{"$f":"yd_-Yt","v":4.185191150112253},{"$f":"TaNTd","v":-0.33592144332876889}]
[-4.2097341558103256,-4.817536741017129,6.1964239585808709,-189.06175978026445,130.10784172662841,7.8488425978309042,87.214622913175958,7.6251611092564664,null,"xd-tx",null,{"$f":"-Spq-KK/v2_x+SIGN(YP_)*KK/v1_x","v":-134.39452481083418},{"$f":"L76-Spq","v":-197.93993241736885}]
[-4.2725660088821211,-4.2577929156507057,6.3980934459975911,-189.06175978026451,122.73992023816184,7.6853367041582938,79.846701424709394,7.2959669875308233,null,null,null,null,null,null,null,{"$f":"-KK/v2_x-SIGN(YP_)*KK/v1_x","v":-60.2528796046888}]
[-4.3353978619539166,-3.6812455268467614,6.5745125815938144,-189.06175978026442,115.9751631419761,7.5349707573728946,73.081944328523647,6.9800641987746621,null,null,null,null,null,null,null,{"$f":"P77/(TANFP-TANFQ)","v":-10.595487293378476}]
[-4.3982297150257121,-3.090169943749459,6.7249851196395776,-189.06175978026448,109.77263870751159,7.4009847412777638,66.87941989405914,6.6772958545636394,null,null,null,null,null,null,null,{"$f":"xd_-Xt","v":-12.458838913764056},null,null,{"$f":"Spq","v":63.54540760653466}]
[-4.4610615680975076,-2.4868988716485356,6.8489172137715766,-189.06175978026448,104.09084443348316,7.2864485861703141,61.197625620030706,6.3873638599989331,null,null,null,null,null,null,null,null,null,null,{"$f":"Spq-KK/v2_x+SIGN(YP_)*KK/v1_x","v":-7.303709597764847}]
[-4.5238934211693032,-1.8738131458572376,6.9458197606334631,-189.06175978026451,98.889105481574589,7.194135657102505,55.995886668122139,6.1098765218358899,null,null,null,null,null,null,null,{"$f":"SAB","v":-7.3037095977648159},null,null,{"$f":"S80-Spq","v":-70.849117204299503}]
[-4.5867252742410987,-1.2533323356430373,7.0153103301433353,-189.06175978026442,94.128477910566957,7.1263890556006153,51.235259097114508,5.8443852882981915,null,null,"SPQ",{"$f":"Spq","v":63.54540760653466},null,{"$f":"v1_x","v":3.7749247904246257},null,null,null,null,{"$f":"S81/(TANFP-TANFQ)","v":-12.45883891376406}]
[-4.6495571273128942,-0.62790519529313205,7.0571146747705571,-189.06175978026442,89.772291661055135,7.0849934698020753,46.879072847602686,5.5904127961837595,null,null,null,{"$f":"SAB","v":-7.3037095977648159},{"$f":"Spq-KK/v2_x+SIGN(YP_)*KK/v1_x","v":-7.303709597764847},{"$f":"v2_x","v":0.30510595546671043}]
[-4.7123889803846897,-1.83772268236293E-15,7.0710678118654755,-189.06175978026448,85.786437626904984,7.0710678118654755,42.893218813452535,5.3474740961474847,null,null,null,{"$f":"SAB","v":-7.3037095977648159},null,{"$f":"v3_x","v":5.3623739219324174}]
[-4.7752208334564852,0.62790519529312827,7.0571146747705571,-189.06175978026448,82.139477504611776,7.0849934698020753,39.246258691159326,5.1150926150728573,null,null,null,null,{"$f":"(M83)/(TANFP-TANFQ)","v":-1.2843595649762396}]
[-4.8380526865282807,1.2533323356430335,7.0153103301433353,-189.06175978026454,78.802634567384587,7.1263890556006144,35.909415753932137,4.8928121262338928]
[-4.9008845396000762,1.873813145857234,6.945819760633464,-189.06175978026448,75.74970756026093,7.194135657102505,32.856488746808481,4.6802057466745683]
[-4.9637163926718717,2.4868988716485321,6.8489172137715775,-189.06175978026454,72.956937814611237,7.2864485861703141,30.063719001158788,4.4768827697523932]
[-5.0265482457436672,3.0901699437494559,6.7249851196395776,-189.06175978026457,70.402850671699909,7.4009847412777621,27.509631858247459,4.2824939663897919]
[-5.0893800988154627,3.6812455268467579,6.5745125815938152,-189.06175978026454,68.068085698605088,7.5349707573728928,25.174866885152639,4.0967358457803646]
[-5.1522119518872582,4.2577929156507022,6.3980934459975929,-189.06175978026457,65.935225400456744,7.6853367041582938,23.042006587004295,3.9193542484278621]
[-5.2150438049590537,4.8175367410171264,6.1964239585808718,-189.06175978026454,63.988628719774091,7.8488425978309024,21.095409906321642,3.7501475443260133]
[-5.2778756580308492,5.3582679497899379,5.9703000166764628,-189.06175978026459,62.214273208366038,8.0221890847120427,19.321054394913588,3.5889696195346086]
[-5.3407075111026447,5.8778525229247016,5.7206140281768594,-189.06175978026451,60.599608087135259,8.2021079693348433,17.706389273682809,3.435732748015849]
[-5.4035393641744403,6.3742398974868655,5.44835138960799,-189.06175978026459,59.133419269975043,8.3854318395272092,16.240200456522594,3.2904103550086874]
[-5.4663712172462358,6.8454710592868544,5.1545865972193212,-189.06175978026462,57.805706668692899,8.569144473736392,14.91248785524045,3.1530395763707597]
[-5.5292030703180313,7.2896862742140822,4.8404790064380414,-189.06175978026468,56.607573605898281,8.7504150180567208,13.714354792445832,3.0237233992155907]
[-5.5920349233898268,7.7051324277578592,4.507268256422857,-189.06175978026462,55.531127861716818,8.9266193413096122,12.637909048264369,2.9026320295281853]
[-5.6548667764616223,8.0901699437494408,4.1562693777745663,-189.06175978026465,54.569393710160284,9.095351827135298,11.676174896707835,2.7900029745154793]
[-5.7176986295334178,8.4432792550201192,3.7888676027110599,-189.06175978026468,53.716234220600413,9.2544304140841938,10.823015407147963,2.6861391633281602]
[-5.7805304826052133,8.7630668004386063,3.4065128981886081,-189.06175978026482,52.966283079701348,9.401897142304561,10.073064266248899,2.5914042867718008]
[-5.8433623356770088,9.0482705246601665,3.010714243544713,-189.06175978026474,52.314885208709228,9.5360159261463586,9.4216663952567785,2.5062144621263331]
[-5.9061941887488043,9.2977648588824877,2.6030336752460488,-189.06175978026477,51.758045495812596,9.6552688044163251,8.864826682360146,2.4310253916622844]
[-5.9690260418205998,9.5105651629515133,2.1850801222441545,-189.06175978026482,51.292385023511322,9.7583515441581365,8.3991662100588727,2.3663144634725217]
[-6.0318578948923953,9.6858316112862912,1.7585030562679145,-189.06175978026502,50.915104239925249,9.8441691879556998,8.0218854264727995,{"$f":"SQRT(2*G105/mass_2)","v":2.3125578084987484}]
[-6.0946897479641908,{"$f":"AA*COS(A106)","v":9.8228725072868723},1.3249859821122121,-189.06175978026494,50.623952596376611,9.9118319269046395,7.7307337829241618,{"$f":"SQRT(2*G106/mass_2)","v":2.2702031895734445}]
[-6.1575216010359863,{"$f":"AA*COS(A107)","v":9.9211470131447683},0.88623979361362837,-189.06175978026488,50.417204248652901,9.9606515363311292,7.5239854352004514,{"$f":"SQRT(2*G107/mass_2)","v":2.2396406609395254}]
[-6.2203534541077818,{"$f":"AA*COS(A108)","v":9.9802672842827107},0.44399602153410023,-189.06175978026482,50.293639494487913,9.9901385141979837,7.4004206810354631,{"$f":"SQRT(2*G108/mass_2)","v":2.2211739660271941}]
[-6.2831853071795774,{"$f":"AA*COS(A109)","v":10},6.4536319908203212E-14,-189.06175978026485,50.252531694167338,10,7.3593128807148886,{"$f":"SQRT(2*G109/mass_2)","v":2.2149962950630999}]

{"sheet":"PROOFS OF PROPERTIES","index":7,"n_rows":7,"n_cols":13,"rows_kept":7,"cut":false,"hidden":false,"merged":[]}
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,"STEP",8]

{"sheet":"propXpV","index":8,"n_rows":109,"n_cols":31,"rows_kept":109,"cut":false,"hidden":false,"merged":[]}
[null,null,null,"xp",{"$f":"7","v":7},"gx",{"$f":"-xp","v":-7},"TGF∙TGY=-B²/A²",null,"PHI",{"$f":"ATAN(yp/xp)","v":0.62493999824450563},{"$f":"TAN(PHI)","v":0.72139320988300537},{"$f":"DEGREES(L1)","v":41.332786295691399},null,null,null,null,null,null,null,"CP",{"$f":"SQRT(xp^2+yp^2)","v":8.6313382508160341},"AA",{"$f":"AA","v":10}]
[null,null,null,"yp",{"$f":"BB*SQRT(1-xp^2/AA^2)","v":5.0497524691810387},"gy",{"$f":"-yp","v":-5.0497524691810387},null,null,"PSI",{"$f":"PI()-K3","v":2.5355103728737856},{"$f":"TAN(PSI)","v":-0.69310328008367272},{"$f":"180-DEGREES(L2)","v":219.71189271546825},null,null,null,null,null,null,null,"CD",{"$f":"SQRT(XD^2+YD^2)","v":8.6890735984913814},"BBT",{"$f":"BB","v":7.0710678118654755},"x=Xcosφ+Ycosψ",null,"xsinφ-ycosφ=Υ(cosψsinφ-sinψcosφ)=Υsin(φ-ψ)"]
[null,null,null,"DYDX",{"$f":"-(xp/yp)*(BB/AA)^2","v":-0.69310328008367217},"RZ",null,null,null,{"$f":"ATAN2(1,-BB^2/AA^2/TAN(PHI))","v":0.60608228071600745},{"$f":"ATAN(-BB^2/AA^2/TAN(PHI))","v":0.60608228071600745},{"$f":"180+DEGREES(K3)","v":214.72595672269043},null,null,"QR IS THE MOVEMENT DUE TO CENTRIPETAL FORCE ",null,null,null,null,null,null,null,null,null,"y=Xsinφ+Ysinψ",null,"xsinψ-ycosψ=X(cosφsinψ-ψcosψsinψ)=Χsin(ψ-φ)"]
[null,null,null,"RX",{"$f":"xp-2.9","v":4.0999999999999996},{"$f":"yp+DYDX*(E4-xp)","v":7.0597519814236884},{"$f":"RX-4","v":9.9999999999999645E-2},{"$f":"yp+DYDX*(G4-xp)","v":9.8321651017583775},null,null,{"$f":"TAN(K3)","v":0.69310328008367239},null,null,null,"SO QR=1/2Ft²","where t is proportionlal to the area  swept by PC =QT*PC",null,null,null,null,"L",{"$f":"COS(PHI)^2/AA^2+SIN(PHI)^2/BB^2","v":1.3422818791946307E-2},"AAT",{"$f":"SQRT(1/V4)","v":8.6313382508160359},null,"RxT",{"$f":"(RX*SIN(PSI)-RY*COS(PSI))/SIN(PSI-PHI)","v":8.6313382508160341},"QXT",{"$f":"AAT*SQRT(1-RYT^2/BBT^2)","v":7.8876361428230597}]
["force to the center of ellipse",null,null,"ZX",{"$f":"xp+3.5","v":10.5},{"$f":"yp+DYDX*(E5-xp)","v":2.6238909888881863},{"$f":"ZX+4","v":14.5},{"$f":"yp+DYDX*(G5-xp)","v":-0.14852213144650239},null,"A",null,"B",null,null,null,"swept by PC =QT*PC",null,null,null,null,"M",{"$f":"COS(PHI)*COS(PSI)/AA^2+SIN(PHI)*SIN(PSI)/BB^2","v":0},null,null,null,"RyT",{"$f":"(RX*SIN(PHI)-RY*COS(PHI))/SIN(PHI-PSI)","v":3.5284696455001132},"QYT",{"$f":"RYT","v":3.5284696455001132},null,"(Xcosφ+Ycosψ)^2/ΑΑ^2+(Xsinφ+Ysinψ)^2/ΒΒ^2=Χ^2*(COSΦ^2/ΑΑ^2+SINΦ^2/ΒΒ^2)+Υ^2*(COSΨ^2/ΑΑ^2+SINΨ^2/BB^2)=1"]
[null,{"$f":"MIN(B9:B109)","v":2.9289321881345254},null,null,null,null,"X²/A²+X²∙TAN(PSI)²/B²=1",null,0,{"$f":"AA","v":10},0,{"$f":"0","v":0},{"$f":"BB","v":7.0710678118654755},0,null,"QR/(PC²∙QT²)",null,null,"FIND Q",null,"N",{"$f":"COS(PSI)^2/AA^2+SIN(PSI)^2/BB^2","v":1.3245033112582783E-2},"BBT",{"$f":"SQRT(1/V6)","v":8.6890735984913832},null,null,null,"QX ",{"$f":"QXT*COS(PHI)+QYT*COS(PSI)","v":3.4968589105566994}]
[null,{"$f":"MAX(B9:B109)","v":17.071067811865476},null,null,null,null,"X²∙(1/A²+TAN(PSI)²/B²)=1",null,null,"MHNYMA5","F~QR/t² ~ QR/(PC²∙QT²) ",null,null,null,"F⌐QR/(PC²∙QT²)",{"$f":"QR/(AAT^2*QT^2)","v":9.019930441769694E-4},"IN THE LIMIT EQUAL",null,null,null,null,null,null,null,null,null,null,"QY ",{"$f":"QXT*SIN(PHI)+QYT*SIN(PSI)","v":6.6246500948978539}]
["FI","R1","x","y",null,null,"X=1/SQRT(1/AA²+(TAN(PSI)/BB)²)",null,null,-4,8,null,null,null,"1/(2∙CD²∙PF²)PC=",{"$f":"1/(2*BBT^2*PF^2)*AAT","v":8.6313382508160317E-4},"1/(2∙CA²∙CB²)PC=R[5]C",{"$f":"1/(2*AA^2*BB^2)*AAT","v":8.6313382508160339E-4},null,null,null,"BF=AAT*COS(φ-ψ)"]
[0,{"$f":"AA*(1-ECCENTRICITY^2)/(1+ECCENTRICITY*COS($A9))","v":2.9289321881345254},{"$f":"CC+B9*COS(A9)","v":10},{"$f":"$B9*SIN($A9)","v":0},{"$f":"SQRT(C9^2+D9^2)","v":10},null,"KX",{"$f":"1/SQRT(1/AA^2+(TAN(PSI)/BB)^2)","v":7.141428428542846},{"$f":"-XK","v":-7.141428428542846},-4,0,null,null,null,"QV²/QT²",{"$f":"QV^2/QT^2","v":1.1249499999999997},"PV",{"$f":"PV","v":0.74370210799297409}]
[{"$f":"A9-PI()/50","v":-6.2831853071795868E-2},2.9313281263187956,9.9966116317251981,{"$f":"$B10*SIN($A10)","v":-0.18405961596244591},{"$f":"SQRT(C10^2+D10^2)","v":9.9983059593999108},null,"YK",{"$f":"-BB*SQRT(1-(XK/AA)^2)","v":-4.9497474683058353},{"$f":"-YK","v":4.9497474683058353},null,null,null,null,null,"PC²/PF²",{"$f":"AAT^2/PF^2","v":1.1249499999999999},"QR",{"$f":"QR","v":0.74370210799297276}]
[{"$f":"A10-PI()/50","v":-0.12566370614359174},2.9385300079671728,9.9864266330234557,-0.36829546782426653,9.993215621029103,null,null,"DK",null,null,null,null,null,null,"QV²",{"$f":"QV^2","v":12.450098039215694},null,null,null,null,null,null,null,null,"FIND V",null,null,null,"QV"]
[-0.1884955592153876,2.9505801847458653,9.969385109594036,-0.55288359380827046,9.9847042886455899,null,null,"QR",null,null,null,"QT is perpendicular to CP",null,null,"QT²/PF²∙PC²",{"$f":"QT^2*AAT^2/PF^2","v":12.450098039215694},null,null,null,null,null,null,null,null,"VXT",{"$f":"QXT","v":7.8876361428230597},"VX",{"$f":"VXT*COS(PHI)+VYT*COS(PSI)","v":6.3968589105566993},{"$f":"QX","v":3.4968589105566994}]
[-0.25132741228718347,2.9675497461125975,9.9453865257616805,-0.73799961151683535,9.9727306477915558,null,{"$f":"QX","v":3.4968589105566994},{"$f":"QY","v":6.6246500948978539},null,null,null,"RQ is the movement due to the force so total movement = PR+RQ",null,null,"2∙QR∙PC",{"$f":"2*QR*AAT","v":12.838288903864528},"will be equal ",null,{"$f":"1/(AA*BB)^2*AAT/2","v":8.631338250816036E-4},null,null,null,null,null,"VYT",{"$f":"0","v":0},"VY",{"$f":"VXT*SIN(PHI)","v":4.6146505826552024},{"$f":"QY","v":6.6246500948978539}]
[-0.31415926535897931,2.9895392816395834,9.9142886263891334,-0.92381844337810337,9.9572365385017587,null,{"$f":"RX","v":4.0999999999999996},{"$f":"RY","v":7.0597519814236884},null,10,6,"MHNYMA2",null,null,"QV²∙PC²/CD²",{"$f":"(QV*AAT/BBT)^2","v":12.285196078431387},"on the limit",null,null,null,null,null,null,null,null,null,"GX",{"$f":"-xp","v":-7}]
[-0.37699111843077515,3.0166799629164114,9.8759059068353956,-1.1105139619414348,9.938146645141293,null,null,"QT",null,10,0,"PR is the velocity: R would be the point where the body would be if there was not any force",null,null,null,null,null,null,null,"QX^2*(1/A^2-2*QX*(T^2*RX-T*RYiRX)/By2+T^2*RX^2",null,null,null,null,null,null,"GY",{"$f":"-yp","v":-5.0497524691810387}]
[-0.43982297150257099,3.0491349597842374,9.8300076100981411,-1.2982585230632289,9.915368112545984,null,{"$f":"QX","v":3.4968589105566994},{"$f":"QY","v":6.6246500948978539},null,4.5,9,"MHNYMA1",null,null,"C",null,null,null,null,null,null,null,null,null,null,null,"VG",{"$f":"SQRT((VX-GX)^2+(VY-GY)^2)","v":16.518974393639095}]
[-0.50265482457436683,3.0871012099871602,9.7763152241487177,-1.4872223502351651,9.888790101977138,null,{"$f":"TX","v":5.4431676353889147},{"$f":"TY","v":3.9266641724244984},null,5,0,"LET P THE POINT WHERE THE BODY PASSES",null,null,0,0,null,null,null,null,null,"VXT",null,null,null,null,"PV",{"$f":"SQRT((xp-VX)^2+(yp-VY)^2)","v":0.74370210799297409}]
[-0.56548667764616267,3.1308115657056654,9.7144994462754557,-1.6775727269352407,9.8582833062274631,null,null,null,null,null,null,"PF is perpendicular to CK",null,null,0,0,null,null,"AA*BB",{"$f":"AA*BB","v":70.710678118654755},null,null,null,null,null,null,"QV",{"$f":"SQRT((QX-VX)^2+(QY-VY)^2)","v":3.5284696455001132}]
[-0.62831853071795851,3.1805373448125187,9.6441765750629749,-1.8694729456462587,9.8236994510976725,null,null,null,null,{"$f":"10","v":10},8.8000000000000007,"mhnyma",null,null,"F⌐QR/(PC²∙QT²)=   1/(2∙CD²∙PF²)∙PC   =     1/(2∙CA²∙PB²)∙CP",null,null,null,"CD∙PF",{"$f":"SQRT(XD^2+YD^2)*SQRT((xp-F_X)^2+(yp-F_Y)^2)","v":70.710678118654755},null,null,null,null,null,"PV∙VG/QV²",{"$f":"PV*VG/QV^2","v":0.98675496688741526}]
[-0.69115038378975435,3.2365913189697872,9.5649042845848555,-2.0630809517236957,9.7848708211521576,null,null,null,null,10,0,"GP, DK CONJUGATE DIAMETERS",null,null,null,null,"MHNYMA7",null,"QR",{"$f":"SQRT((QX-RX)^2+(QY-RY)^2)","v":0.74370210799297276},null,null,null,null,null,"PC²/CD²",{"$f":"(xp^2+yp^2)/(XD^2+YD^2)","v":0.98675496688741759}]
[-0.75398223686155019,3.2993311747068352,9.4761767297001906,-2.2585476071458643,9.7416098621457685,null,null,null,null,null,null,"mhnyma3","2QR∙PC∙CD²∙PF²",null,null,null,12,3.5,"QT",{"$f":"SQRT((QX-TX)^2+(QY-TY)^2)","v":3.326747013258208},null,null,null,null,null,"We have CV²/CP² + QV²/CD² = 1 But CV=PC-VP so   1- 2VP∙PC/ CP²+VP²/CP²+ QV²/CD²=1    We use 2PC=GP and VP²-GP∙VP  =VP∙(VP-GP)and GP-VP=VG so  QV²/CD²= VG∙VP/PC² or  PV∙VG/QV² = PC²/CD²"]
[-0.81681408993334603,3.3691634871293088,9.3774189263804519,-2.4560144827709882,9.6937089321074179,null,null,null,null,10,-1,null,"Since CP∙PF=CA∙CB = constant so ",null,null,null,12,-1,"VG",null,null,null,null,null,null,"mhnyma4",null,null,"∆PCF is similar to ∆QVT because angle PCF=angle QVT who are equal to the angles of conjugate diameters. So QV²/QT²=PC²/PF² so QV²=QT²∙PC²/PF²"]
[-0.87964594300514187,3.4465482485211107,9.2679803472991598,-2.655611067351217,9.6409402995227449,null,null,null,null,10,-5,null,"QV²/QT²=PC²/PF² so QV²=QT²∙PC²/PF²",null,null,null,null,"Making these combinations and multiplying by  QV²: PV∙VG =QV² PC²/CD² or 2∙QR∙PC=QV²∙PC²/CD² and since QV²=QT²∙PC²/PF²",null,null,null,null,null,null,null,{"$f":"10","v":10},-4.5,null,"Since PVQR is a parallelogram, PV= QR. And VG→2∙PC That is VG =2 PC in the limit."]
[-0.94247779607693771,3.5320039952404718,9.1471276713059186,-2.8574512563497518,9.5830565227168112,null,null,null,null,null,null,null,null,null,null,null,"mhnyma6",null,null,null,null,null,null,null,null,10,-8,null,"mhnyma6","X`"]
[-1.0053096491487337,3.6261135751401024,9.0140366270626266,-3.0616289525327374,9.5197913925155557,null,null,null,null,null,"Cut of two lines y=y1+t1*(x-x1)",null,null,"SSAA","=Y2-Y1+X1*T1-X2*T2",null,-15,5,null,null,null,null,null,null,null,null,null,null,10,1]
[-1.0681415022205296,3.7295305930564386,8.8677828777451637,-3.2682125721233093,9.4508616847044777,null,null,null,null,null,null,"y=y2+t2*(x-x2)",null,"XLSH","=SSAA/(T1-T2)",null,-15,2,null,null,null,null,null,null,null,null,null,null,10,-1]
[-1.1309733552923256,3.8429865620027552,8.7073319077291025,-3.4772382035634752,9.3759700551824867,null,null,null,null,null,null,"FIND PF PERPENDICULA TO DK",null,null,null,"FP"]
[-1.1938052083641215,3.9672987701529769,8.5315278969945112,-3.6887011089816166,9.2948095262139603,null,null,null,null,null,null,"SSAA",{"$f":"YD-yp+xp*(-1/TAN(PSI))-XD*TAN(PSI)","v":5.049752469181028},"F_X",{"$f":"M28/(-1/TAN(PSI)-TAN(PSI))","v":2.3642384105960224},"F_Y",{"$f":"yp-1/TAN(PSI)*(O28-xp)","v":-1.6386613972839124}]
[-1.2566370614359175,4.1033788451439088,8.3390816093735882,-3.9025451895017969,9.2070701661221417,null,null,null,null,null,null,null,null,"XP",{"$f":"xp","v":7},"YP",{"$f":"yp","v":5.0497524691810387}]
[-1.3194689145077134,4.2522419529710076,8.1285573833474949,-4.1186499526924427,9.1124487689745912,null,null,null,null,null,null,"FIND THE PERPENDICULAR QT TO PG"]
[-1.3823007675795094,4.4150165023581609,7.898359407995013,-4.3368144220231892,9.010662609871245,null,null,null,null,null,null,"T1",{"$f":"-1/TAN(PHI)","v":-1.3862065601673443},"X1",{"$f":"QX","v":3.4968589105566994},"Y1",{"$f":"QY","v":6.6246500948978539}]
[-1.4451326206513053,4.5929541281400592,7.6467176043577858,-4.5567373129907729,8.9014687024331902,null,null,null,null,null,null,"T2",{"$f":"TAN(PHI)","v":0.72139320988300537},"X2",{"$f":"xp","v":7},"Y2",{"$f":"yp","v":5.0497524691810387}]
[-1.5079644737231013,4.787439587003588,7.3716736307486288,-4.7779926685651866,8.7846904361586553,null,null,null,null,null,null,"SSAA",{"$f":"yp-QY+(-1/TAN(PHI))*QX-TAN(PHI)*xp","v":-11.472018856691182},"XLYSH",{"$f":"M33/(-1/TAN(PHI)-TAN(PHI))","v":5.4431676353889147},"YLYSH",{"$f":"QY-1/TAN(PHI)*(TX-QX)","v":3.9266641724244984}]
[-1.5707963267948972,5.0000000000000036,7.071067811865472,-5.0000000000000036,8.6602540378443855]
[-1.6336281798666932,5.2323125976792033,6.7425281855174228,-5.2219878239758062,8.5282379871957392]
[-1.6964600329384891,5.4862097386502162,6.3834634053084622,-5.442949336209538,8.3889392966844252]
[-1.7592918860102851,5.7636794473069726,5.9910619801783662,-5.6615888383766126,8.2429613504595167]
[-1.822123739082081,6.0668590113385026,5.562301328890614,-5.876257479323967,8.0913285705555893]
[-1.884955592153877,6.3980182499782554,5.0939714423011271,-6.0848769480171319,7.9356330892682854]
[-1.9477874452256729,6.7595278665355982,4.5827196396374346,-6.2848500660111748,7.7782169967004213]
[-2.0106192982974687,7.153806804052885,{"$f":"CC+B41*COS(A41)","v":4.0251250188424343},-6.4729579244225244,7.6223891076653691]
[-2.0734511513692646,7.5832407386166789,3.4178137244390774,-6.6452445156305533,7.4726652091126136]
[-2.1362830044410606,8.0500618569689433,2.7576289676631287,-6.7968920278574814,7.335002301407096]
[-2.1991148575128565,8.5561781047598302,2.0418725058998746,-6.9220934936495251,7.2169676225666217]
[-2.2619467105846525,9.1029386349454793,1.2686363487410262,-7.0139347664008493,7.1277429171283595]
[-2.3247785636564484,9.690822086466893,0.43724359850473604,-7.0643052749568609,7.077823887482416]
[-2.3876104167282444,10.319036962110586,-0.45118639871510169,-7.0638668883839575,7.0782614096395706]
[-2.4504422698000403,10.985030761347291,-1.3930438620520347,-7.0021221354100636,7.1393477013520243]
[-2.5132741228718363,11.683919218601932,-2.3814213968875579,-6.8676354056707973,7.2688089763576116]
[-2.5761059759436322,12.407871605062248,-3.4052446803321041,-6.6484700746513834,7.4697955572067078]
[-2.6389378290154282,13.145523963639432,-4.4484426501484586,-6.3329044674754185,7.7391421362984376]
[-2.7017696820872241,13.88153724988795,-5.4893226216479052,-5.9104710960914337,8.066370399520947]
[-2.7646015351590201,14.596462894983874,-6.5003801650308946,-5.3733163739944105,8.4337104020095168]
[-2.827433388230816,15.267106204567044,-7.4488130289581926,-4.717795272138388,8.8171655179081583]
[-2.890265241302612,15.867561531077943,-8.2979850953090697,-3.9461020867451304,9.1884861822275017]
[-2.9530970943744079,16.371005009963149,-9.0099616910368212,-3.0676204398563418,9.5178624090168231]
[-3.0159289474462039,16.752160368619222,-9.5489967686194213,-2.0996024281867949,9.7770992448451715]
[-3.0787608005179998,16.990128555587447,-9.885534606043219,-1.0668189988751169,9.9429320234847722]
[-3.1415926535897958,17.071067811865476,-10,4.3395002859874335E-14,10]
[-3.2044245066615917,16.99012855558744,-9.8855346060432083,1.0668189988752026,9.9429320234847705]
[-3.2672563597333877,16.752160368619201,-9.5489967686193893,2.0996024281868766,9.777099244845159]
[-3.3300882128051836,16.371005009963117,-9.009961691036775,3.0676204398564177,9.5178624090168036]
[-3.3929200658769796,15.867561531077898,-8.2979850953090057,3.9461020867451975,9.1884861822274733]
[-3.4557519189487755,15.267106204566993,-7.4488130289581198,4.7177952721384457,8.8171655179081281]
[-3.5185837720205715,14.596462894983818,-6.5003801650308146,5.3733163739944585,8.4337104020094849]
[-3.5814156250923674,13.88153724988789,-5.4893226216478199,5.9104710960914719,8.0663703995209151]
[-3.6442474781641634,13.14552396363937,-4.4484426501483716,6.3329044674754469,7.7391421362984119]
[-3.7070793312359593,12.407871605062185,-3.4052446803320171,6.6484700746514038,7.4697955572066856]
[-3.7699111843077553,11.683919218601872,-2.3814213968874727,6.8676354056708098,7.2688089763575947]
[-3.8327430373795512,10.985030761347238,-1.3930438620519583,7.0021221354100724,7.1393477013520181]
[-3.8955748904513472,10.319036962110534,-0.45118639871502886,7.0638668883839602,7.078261409639568]
[-3.9584067435231431,9.6908220864668415,0.43724359850480798,7.0643052749568565,7.077823887482416]
[-4.0212385965949391,{"$f":"AA*(1-ECCENTRICITY^2)/(1+ECCENTRICITY*COS($A73))","v":9.1029386349454313},{"$f":"CC+B73*COS(A73)","v":1.2686363487410928},7.0139347664008422,7.1277429171283639]
[-4.0840704496667346,8.5561781047597911,2.0418725058999296,{"$f":"$B74*SIN($A74)","v":6.922093493649518},{"$f":"SQRT(C74^2+D74^2)","v":7.2169676225666306}]
[{"$f":"A74-PI()/50","v":-4.1469023027385301},8.0500618569689113,2.7576289676631731,6.7968920278574734,7.3350023014071057]
[-4.2097341558103256,7.5832407386166514,3.4178137244391156,6.6452445156305435,7.4726652091126224]
[-4.2725660088821211,7.1538068040528637,4.0251250188424645,6.4729579244225146,7.6223891076653763]
[-4.3353978619539166,6.7595278665355805,4.5827196396374603,6.2848500660111659,7.7782169967004293]
[-4.3982297150257121,6.3980182499782412,5.0939714423011475,6.0848769480171248,7.9356330892682934]
[-4.4610615680975076,6.066859011338491,5.56230132889063,5.876257479323959,8.0913285705555946]
[-4.5238934211693032,5.7636794473069646,5.9910619801783778,5.6615888383766073,8.2429613504595203]
[-4.5867252742410987,5.4862097386502109,6.3834634053084702,5.4429493362095336,8.3889392966844269]
[-4.6495571273128942,5.2323125976791998,6.7425281855174273,5.2219878239758026,8.528237987195741]
[-4.7123889803846897,5.0000000000000018,7.0710678118654737,5.0000000000000018,8.6602540378443873]
[-4.7752208334564852,4.787439587003588,7.3716736307486288,4.7779926685651866,8.7846904361586553]
[-4.8380526865282807,4.5929541281400601,7.646717604357784,4.5567373129907747,8.9014687024331902]
[-4.9008845396000762,4.4150165023581636,7.8983594079950095,4.3368144220231928,9.0106626098712432]
[-4.9637163926718717,4.2522419529710112,8.1285573833474913,4.118649952692448,9.1124487689745912]
[-5.0265482457436672,4.1033788451439124,8.3390816093735811,3.9025451895018022,9.2070701661221381]
[-5.0893800988154627,3.9672987701529809,8.5315278969945059,3.6887011089816237,9.2948095262139585]
[-5.1522119518872582,3.8429865620027606,8.7073319077290954,3.4772382035634841,9.3759700551824832]
[-5.2150438049590537,3.729530593056444,8.8677828777451566,3.2682125721233195,9.4508616847044742]
[-5.2778756580308492,3.6261135751401081,9.0140366270626195,3.0616289525327494,9.519791392515554]
[-5.3407075111026447,3.5320039952404776,9.1471276713059115,2.8574512563497652,9.5830565227168076]
[-5.4035393641744403,3.4465482485211165,9.2679803472991527,2.6556110673512312,9.6409402995227431]
[-5.4663712172462358,3.3691634871293146,9.3774189263804448,2.4560144827710033,9.6937089321074161]
[-5.5292030703180313,3.2993311747068401,9.4761767297001818,2.2585476071458794,9.741609862145765]
[-5.5920349233898268,3.2365913189697921,9.5649042845848466,2.0630809517237121,9.7848708211521505]
[-5.6548667764616223,3.1805373448125231,9.6441765750629678,1.8694729456462758,9.823699451097669]
[-5.7176986295334178,3.1308115657056699,9.7144994462754486,1.6775727269352592,9.8582833062274595]
[-5.7805304826052133,3.0871012099871646,9.7763152241487123,1.4872223502351845,9.8887901019771345]
[-5.8433623356770088,3.049134959784241,9.8300076100981357,1.2982585230632486,9.9153681125459805]
[-5.9061941887488043,3.0166799629164149,9.875905906835392,1.1105139619414557,9.9381466451412912]
[-5.9690260418205998,2.989539281639586,9.9142886263891281,0.92381844337812513,9.9572365385017534]
[-6.0318578948923953,2.9675497461125997,{"$f":"CC+B105*COS(A105)","v":9.9453865257616769},0.737999611516858,9.972730647791554]
[-6.0946897479641908,2.9505801847458666,{"$f":"CC+B106*COS(A106)","v":9.9693851095940342},0.5528835938082941,9.9847042886455899]
[-6.1575216010359863,2.9385300079671741,{"$f":"CC+B107*COS(A107)","v":9.9864266330234557},0.36829546782429118,9.9932156210291048]
[-6.2203534541077818,2.9313281263187965,{"$f":"CC+B108*COS(A108)","v":9.9966116317251963},0.18405961596247164,9.9983059593999108]
[-6.2831853071795774,2.9289321881345254,{"$f":"CC+B109*COS(A109)","v":10},2.6731818971626555E-14,10]