Classical Mechanics According to Newton and Hamilton

This chapter introduces classical mechanics, starting with the familiar definitions of position, momentum, velocity, acceleration force, kinetic, potential, and total energy. It is shown how the Newton equation of motion is solved for the one-dimensional harmonic oscillator, which is a point mass oscillating around the position x = 0 driven by a force that is proportional to x (Hooke’s law). Next, the minimal action principle, the Lagrange equation of motion, and the classical Hamilton function (Hamiltonian) and conjugated variables are introduced. The chapter also discusses angular momentum and rotational motion.