I'm not sure exactly where to start because I can't figure out what the initial values are for the Runge-Kutta. I want to solve this in Python. Thanks in advance.
Programming Assignment 2: Two Masses Motion Simulation
Consider two masses m1 and m2 which are at time t in the positions x1 and x2. According to Newton's law of gravitation, the mass m1 attracts the mass m2 with the force F = G * (m1 * m2) / r^2, where G is the gravitational constant. The attraction force of m2 on m1 is F = -F.
Let v1(t) and v2(t) be the velocities of the masses m1 and m2 at time t, respectively. Then, according to Newton's second law, m1 * a1 = F and m2 * a2 = -F, where a1 and a2 are the accelerations of m1 and m2, respectively.
The motion of the masses is described by the system of ordinary differential equations:
dx1/dt = v1(t)
dx2/dt = v2(t)
dv1/dt = F1(t)/(m1 * v1(t))
dv2/dt = F2(t)/(m2 * v2(t))
We can solve this system using a classical Runge-Kutta method and generate an animation showing the motion of the masses. Assume all vectors are 2-dimensional (plane motion). The parameter h is the time step size, and the parameter p determines the initial velocities.
Write a Python function twomasses(m1, m2, x1, x2, p, h) which solves the system using a classical Runge-Kutta method and generates an animation showing the motion of the masses. Assume the gravitational constant is G = 1.
Hint: First, write a function runge_kutta_step(h, f) to compute one Runge-Kutta step with step size h for a differential equation with an arbitrary right side f (not explicitly depending on time).
