I n the previous lectures we saw that the orbits of particles under the influence of central forces have certain simple properties. The orbit is restricted to a plane and we can write down simple equations for the conservation of energy and angular momentum. Orbits are either bound or unbound , depending on whether they have a kinetic energy greater than the potential energy.
Some orbits are closed and always return to their starting point, while others are open .
We looked at two examples of central forces, the central harmonic oscillator and the Keplerian force field. This is not so in general however. Usually, for any realistic potential field, the orbit is complicated and does not admit of simple or general solutions, even if the potential does not change with time. We will see some chaotic orbits later on in the course. In this lecture we will examine the numerical techniques used to solve for orbits when the analytic solution is not known.