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I have used the Equation of Motion (Newtons Law) for a simple spring and mass scenario incorporating it into the given 2nd ODE equation y" + (k/m)x = 0; y(0) = 3; y'(0) = 0.

I have then been able to run a code that calculates and compares the Exact Solution with the Runge-Kutta Method Solution.

It works fine...however, I have recently been asked not to separate my values of 'x' and 'v', but use a single vector 'x' that has two dimensions ( i.e. 'x' and 'v' can be handled by x(1) and x(2) ).

MY CODE:

I am trying to make a python program which plot pendulum swings using runge kutta 4. The equation I have is angular accelartion = -(m*g*r/I) * np.sin(y).

Please find my code. I am quite new to python.

I'm trying to implement an RK4 method to solve for the orbit of a rocket around the Earth. Eventually this code will be used for more complex solar system simulations, but I'm just trying to get it working in this simple system first. My code is below - I'm hoping someone can tell me what is wrong with it. My trouble-shooting efforts have been long and unfruitful, but I'll summarise what I've found:

• I believe the acceleration function is fine and correct, as it gives believable values and agrees with my calculator/brain

• It appears as though the problem lies somewhere in the calculation of the next "r" value - when you run this code, an x-y graph will appear, showing that the rocket initially falls in towards the Earth, then bounces away again, then back. I printed all the relevant values at this point, and found that "v" and "a" were negative in both components, despite the rocket clearly moving in the positive y direction. This makes me think that the calculation of the new "r" is in disagreement with the physics.

• The rocket is falling to Earth much faster than it should, which is also suspicious (technically it shouldn't fall into Earth at all, since the initial velocity is set to the required orbital velocity)

Either way I would greatly appreciate if anyone could find the error, as I have been unable up to this point.