Newtonian Mechanics

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.

Watch and play with Cosmic Interaction.

Test different forces fx and fy with different dependence on x, y, vx and vy.

What happened?