Models from Classical Mechanics

The goal of this section is to familiarize ourselves with the use of differential equations as models, to discuss scalings and dimensional analysis, and to introduce phase plane techniques. This will be done on examples of application of classical mechanics.

In the first chapter, we will go over the derivation of the equation of motion of the nonlinear pendulum, check the dimension of each term in this equation, discuss the limit of small oscillations, and investigate the nonlinear dynamics of the pendulum by means of phase plane analysis.

We will then consider the problem of stone-skipping, and introduce Euler’s equation for the dynamics of a rigid body. This discussion will also provide a good illustration of the power of dimensional analysis.