Session 9

Newton’s Mechanics

The basic model is the 1d Harmonic Oscillator

  • f(x) = -x,  dv/dt = f(x), dx/dt = v for t > 0,

with solution x(t) = A*sin(t) + B*cos(t) with coefficients A and B determined by B = x(0) and A = v(0). Here f(x) = -x  is a linear spring force. Write code for non-linear spring force e g f(x) = -x^3.

Newton’s gravitational force f(x) from a point mass at x = 0 in 3d is given as the gradient of the gravitational potential = 1/|x|, that is

  • f(x) = -x/|x|^3.

Write 2d code for the motion of one body subject to f(x).

Test with different gravitational forces

  • f(x) = -x/|x|^p

with different p (help: Variants of Newton’s Gravitational Model).