Applications in Mechanics

This chapter delves into some systems of differential equations arising in mechanics. The first is the famous Newton's second law, force = mass × acceleration. This leads to the more general type of systems known as conservative systems, which are special examples of Hamiltonian systems as described in Chapter 9 . The main example here is given by central force fields and, specifically, the Newtonian central force system. Specific examples treated include Kepler's first law and the two-body problem from celestial mechanics. A new technique called blowing up the singularity provides a tool for understanding these systems near places where the system is undefined–that is, collisions between the various bodies. Explorations include classical limits of quantum mechanical systems and the motion of a glider.