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Position and velocity vectors are calculated by integrating the perturbed equation of motion (Cowell's equation). To update the state vectors, equation (9) is integrated numerically by using 4th order Runge-Kutta's as [11]: h Xo + (k₁ + 2 k₂ + 2k + k₁₂ ) step 6 (17) where vxo is the initial velocity at epoch, vx₁ is the predicated velocity, k₁ = axo, k₂ hstep = axo -k₁, k₁ = ax。+ k₂, ka xo+ hstep h3,, axo is the acceleration at epoch, 2 h. step 2 t step hstep is the step for the method, tstep m = Τ m is the sub steps number during one nnn revolution the used values 10,20,30,40, and 50, Tp is the satellite's orbital period, the used value 5317.5 second, and nnn is the step number during 400 revolutions, the used value is 800,1000,1200,1400, 1600, and 1800. X₁ = X + Вер 6 - hep (kk, +2 kk₂+ 2 kk, + kk₁) (18) where X is the initial position at epoch, X₁ is the predicated position, kk₁ = vx, kk₂ = vx+ hap kk,, kk, = vxo+ h 2 step 2 -kk₂, kk₁ = vxo+hstep kk3. In addition, Equations (17) and (18) can be used to calculate the other velocities and positions components by the same way.

Position and velocity vectors are calculated by integrating the perturbed equation of motion (Cowell's equation). To update the state vectors, equation (9) is integrated numerically by using 4th order Runge-Kutta's as [11]: h Xo + (k₁ + 2 k₂ + 2k + k₁₂ ) step 6 (17) where vxo is the initial velocity at epoch, vx₁ is the predicated velocity, k₁ = axo, k₂ hstep = axo -k₁, k₁ = ax。+ k₂, ka xo+ hstep h3,, axo is the acceleration at epoch, 2 h. step 2 t step hstep is the step for the method, tstep m = Τ m is the sub steps number during one nnn revolution the used values 10,20,30,40, and 50, Tp is the satellite's orbital period, the used value 5317.5 second, and nnn is the step number during 400 revolutions, the used value is 800,1000,1200,1400, 1600, and 1800. X₁ = X + Вер 6 - hep (kk, +2 kk₂+ 2 kk, + kk₁) (18) where X is the initial position at epoch, X₁ is the predicated position, kk₁ = vx, kk₂ = vx+ hap kk,, kk, = vxo+ h 2 step 2 -kk₂, kk₁ = vxo+hstep kk3. In addition, Equations (17) and (18) can be used to calculate the other velocities and positions components by the same way.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter4: Numerical Analysis Of Heat Conduction
Section: Chapter Questions
Problem 4.6P
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The attached image is of the Runge-Kutta method. I want to know if there are any errors with the equations. I think I saw an error on k2 equation. It should be k2 = ax0 + h_step/2 * k1, right? Please let me know if there is anything else wrong with it

Position and velocity vectors are calculated by integrating the perturbed equation of motion (Cowell's equation). To update the state vectors, equation (9) is integrated numerically by using 4th order Runge-Kutta's as [11]: h Xo + (k₁ + 2 k₂ + 2k + k₁₂ ) step 6 (17) where vxo is the initial velocity at epoch, vx₁ is the predicated velocity, k₁ = axo, k₂ hstep = axo -k₁, k₁ = ax。+ k₂, ka xo+ hstep h3,, axo is the acceleration at epoch, 2 h. step 2 t step hstep is the step for the method, tstep m = Τ m is the sub steps number during one nnn revolution the used values 10,20,30,40, and 50, Tp is the satellite's orbital period, the used value 5317.5 second, and nnn is the step number during 400 revolutions, the used value is 800,1000,1200,1400, 1600, and 1800. X₁ = X + Вер 6 - hep (kk, +2 kk₂+ 2 kk, + kk₁) (18) where X is the initial position at epoch, X₁ is the predicated position, kk₁ = vx, kk₂ = vx+ hap kk,, kk, = vxo+ h 2 step 2 -kk₂, kk₁ = vxo+hstep kk3. In addition, Equations (17) and (18) can be used to calculate the other velocities and positions components by the same way.
Transcribed Image Text:Position and velocity vectors are calculated by integrating the perturbed equation of motion (Cowell's equation). To update the state vectors, equation (9) is integrated numerically by using 4th order Runge-Kutta's as [11]: h Xo + (k₁ + 2 k₂ + 2k + k₁₂ ) step 6 (17) where vxo is the initial velocity at epoch, vx₁ is the predicated velocity, k₁ = axo, k₂ hstep = axo -k₁, k₁ = ax。+ k₂, ka xo+ hstep h3,, axo is the acceleration at epoch, 2 h. step 2 t step hstep is the step for the method, tstep m = Τ m is the sub steps number during one nnn revolution the used values 10,20,30,40, and 50, Tp is the satellite's orbital period, the used value 5317.5 second, and nnn is the step number during 400 revolutions, the used value is 800,1000,1200,1400, 1600, and 1800. X₁ = X + Вер 6 - hep (kk, +2 kk₂+ 2 kk, + kk₁) (18) where X is the initial position at epoch, X₁ is the predicated position, kk₁ = vx, kk₂ = vx+ hap kk,, kk, = vxo+ h 2 step 2 -kk₂, kk₁ = vxo+hstep kk3. In addition, Equations (17) and (18) can be used to calculate the other velocities and positions components by the same way.
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