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[0,null,"time",{"$f":"AF2*dt","v":0.88},null,null,null,null,"current x","currenty","For the rotating frame: aX = Ax·cosωt+Ay sinωΤ+2Ω(-Vx*sinωt+Vy cosωt)-ω² (X cosωt+Y sinωt)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,88,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"taxXom(kkk) = (taxYx(kkk) - omega * thesiY(kkk)) * Cos(thesiG(kkk)) - (taxYy(kkk) + omega * thesiX(kkk) * Sin(thesiG(kkk)))"]
[null,null,null,null,null,null,null,null,{"$f":"D12","v":0.91211547908705082},{"$f":"E12","v":0.27736252456507632},null,null,"ay = -Ax sinωt+Ay cosωt+2ω( -Vx cosωt-Vy sinωt) -ω²(-X sinωt+Ycosωt)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"taxYom(kkk) = (taxYx(kkk) - omega * thesiY(kkk)) * Sin(thesiG(kkk)) - (taxYy(kkk) + omega * thesiX(kkk) * Cos(thesiG(kkk)))"]
["g",9.81,null,{"$f":"VLOOKUP(D2,A17:E467,2)","v":0.91211547908705082},null,null,null,null,70,70,null,null,"vxom","vyom",null,"x=X*cosωt+Y*sinωt",null,"vx=Vx*cosωτ-ωX*sinωt+Vy*sinωt+ωY*cosωt",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,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,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,null,null,null,"thesiXom(kkk) = thesiX(kkk) * Cos(thesiG(kkk)) - thesiY(kkk) * Sin(thesiG(kkk))"]
["statherifoucault",30,null,"TEXTBOOK","NO","YES IF IT IS AS IN TEXTBOOKS",null,null,null,null,null,null,null,null,null,"y=-X*sinωt+Y*cosωt",null,"vy=-Vx*sinωt-ωX*cosωt+Vy*cosωt-ωY*sinωt"]
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["v0",{"$f":"IF(TEXTBOOK=\"YES\",0,omega*R0)","v":-5},null,"current ax","current ay","cuurent axo","current ayo",null,"vx","vy","ax","ay","vxom","vyom",null,null,"axom","ayom",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"AXOM-=(AX-OMEGA*VY)*COS(F)-(VX-OMEG*Y)*SIN(F)*OMEGA-(AY+OMEGA*VX)*SIN(F)-(VY+OMEGA*X)*COS(F)*OMEGA"]
["R0",5,null,{"$f":"VLOOKUP($D$2,$A$16:L464,11)","v":-27.363464372611524},{"$f":"VLOOKUP($D$2,$A$16:$L$464,12)","v":-8.3208757369522903},{"$f":"AX_CUR*COS(omega*$D$2)+AY_CUR*SIN(omega*$D$2)+2*omega*(-VX_CUR*SIN(omega*$D$2)+VY_CUR*COS(omega*$D$2))-omega^2*(X_CUR*COS(omega*$D$2)+Y_CUR*SIN(omega*$D$2))","v":-46.826786570993789},{"$f":"-AX_CUR*SIN(omega*$D$2)+AY_CUR*COS(omega*$D$2)+2*omega*(-VX_CUR*COS(omega*$D$2)-VY_CUR*SIN(omega*$D$2))-omega^2*(-X_CUR*SIN(omega*$D$2)+Y_CUR*COS(omega*$D$2))","v":-70.899024429832707},null,{"$f":"D12","v":0.91211547908705082},{"$f":"E12","v":0.27736252456507632},{"$f":"D12","v":0.91211547908705082},{"$f":"E12","v":0.27736252456507632},{"$f":"F12","v":0.15970726517847167},{"$f":"G12","v":1.0536627697282492},null,null,{"$f":"F12","v":0.15970726517847167},{"$f":"G12","v":1.0536627697282492},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(12/13-3/8)dt",null,null,null,null,null,null,null,null,null,null,null,null,"(1-12/13)dt",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"AYOM=(AX-OMEGA*VY)*SIN(F)-(VX-OMEGA*Y)*COS(F)*OMEGA-(AY_OMEGA*vx)*cos(f)+(vy+OMEGA*X)*SIN(F)*OMEGA"]
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["mew",0,null,{"$f":"VLOOKUP($D$2,$A$17:L464,4)","v":-0.24196564617228453},{"$f":"VLOOKUP($D$2,$A$17:$L$467,5)","v":28.102397697616361},{"$f":"VLOOKUP($D$2,A17:DP467,15)","v":-22.511508605883279},{"$f":"VLOOKUP($D$2,A17:DP467,16)","v":18.312390802876081},null,{"$f":"-1/20*J6+18/20*I6+I8","v":0.58753768579987597},{"$f":"1/20*I6+18/20*J6+J8","v":5.3333744536742982},{"$f":"-1/20*L6+18/20*K6+K8","v":-0.2984382283380872},{"$f":"1/20*K6+18/20*L6+L8","v":-0.16548554452930553},{"$f":"-1/20*N6+18/20*M6+M8","v":-4.0754881919092796},{"$f":"1/20*M6+18/20*N6+N8","v":4.1247780281871114},null,null,{"$f":"-1/20*R6+18/20*Q6+Q8","v":-1.770250569441667},{"$f":"1/20*Q6+18/20*R6+R8","v":-2.2538602960417071},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AX18-AL18","v":5.4807692307692318E-3},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"     k1(I) = deltax * MyRelFx(x, y(), I, Vxframe0, Vyframe0, synTELetrivis)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"     k4(I) = deltax * MyRelFx(x + 12# / 13 * deltax, y(), I, Vxframe0, Vyframe0, synTELetrivis)"]
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[]
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{"sheet":"Φύλλο3","index":2,"n_rows":55,"n_cols":1,"rows_kept":55,"cut":false,"hidden":false,"merged":[]}
[]
["Sub VectRungeKuttaFehlberg(x0 As Double, y0() As Double, deltaX As Double, y1() As Double, numYVar As Integer)"]
[]
["  Dim x As Double, halfDelta As Double"]
["  Dim Y() As Double"]
["  Dim k1() As Double, k2() As Double"]
["  Dim k3() As Double, k4() As Double"]
["  Dim k5() As Double"]
["  Dim i As Integer"]
[]
["  If numYVar < 1 Then Exit Sub"]
[]
["  ' allocate local dynamic arrays"]
["  ReDim k1(numYVar)"]
["  ReDim k2(numYVar)"]
["  ReDim k3(numYVar)"]
["  ReDim k4(numYVar)"]
["  ReDim k5(numYVar)"]
["  ReDim Y(numYVar)"]
[]
["  x = x0"]
["  For i = 0 To numYVar - 1"]
["     Y(i) = y0(i)"]
["  Next i"]
["  For i = 0 To numYVar - 1"]
["     k1(i) = deltaX * MyArrFx(x, Y(), i)"]
["  Next i"]
["  For i = 0 To numYVar - 1"]
["     Y(i) = y0(i) + k1(i) / 4"]
["  Next i"]
["  For i = 0 To numYVar - 1"]
["     k2(i) = deltaX * MyArrFx(x + deltaX / 4, Y(), i)"]
["  Next i"]
["  For i = 0 To numYVar - 1"]
["     Y(i) = y0(i) + 3# / 32 * (k1(i) + 3 * k2(i))"]
["  Next i"]
["  For i = 0 To numYVar - 1"]
["     k3(i) = deltaX * MyArrFx(x + 3# / 8 * deltaX, Y(), i)"]
["  Next i"]
["  For i = 0 To numYVar - 1"]
["     Y(i) = y0(i) + 1932# / 2197 * k1(i) - 7200# / 2197 * k2(i) + 7296# / 2197 * k3(i)"]
["  Next i"]
["  For i = 0 To numYVar - 1"]
["     k4(i) = deltaX * MyArrFx(x + 12# / 13 * deltaX, Y(), i)"]
["  Next i"]
["  For i = 0 To numYVar - 1"]
["     Y(i) = y0(i) + 439# / 216 * k1(i) - 8 * k2(i) + 3680# / 513 * k3(i) - 845# / 4104 * k4(i)"]
["  Next i"]
["  For i = 0 To numYVar - 1"]
["     k5(i) = deltaX * MyArrFx(x + deltaX, Y(), i)"]
["  Next i"]
["  For i = 0 To numYVar - 1"]
["     y1(i) = y0(i) + 25# / 216 * k1(i) + 1408# / 2565 * k3(i) + 2197# / 4104 * k4(i) - k5(i) / 5"]
["  Next i"]
["End Sub"]