Newton’s Mechanics in a plane with (x,y)-coordinates has the form, see Header,
- x = x + vx* dt, y = y + vy*dt
- vx = vx +ax*dt, vy = vy + ay*dt,
- ax = fx/m, ay = fy/m (Newton’s 2nd Law: f = a*m with f force, a acceleration and m mass)
- fx and fy forces depending on x, y, vx and vy, and m mass,
where vx and vy are velocities as rates of change of position x and y and ax and ay are accelerations as rates of change of vx and vy.
This is the time stepping form of the differential equations (compare with Header):
- dx/dt = vx, dy/dt = vy, or: dx = vx*dt, dy = vy*dt (multiplying by dt)
- dvx/dt = ax, dvy/dt = ay, or: dvx =ax*dt, dvy = ay*dt.
Test different forces fx and fy with different dependence on x, y, vx and vy.