Synopsis for Classical Mechanics

Overview

This course extends the study of the dynamics of point particles in the first year to the study of extended rigid bodies moving in three dimensions.

The course provides powerful applications of the Lagrangian theory to a range of systems, in particular to the study of small oscillations near equilibrium, and it introduces some key classical ideas that also play an important role in modern physical theory, notably angular momentum and its connection with rotations.

Synopsis

Lagrangian equations of motion with and without holonomic constraints. Oscillations near equilibrium; normal frequencies, normal modes.

Angular momentum of a system of particles about a fixed point and about the centre of mass. The description of the motion of a rigid body with one fixed point in terms of a time-dependent rotation matrix. Definition of angular velocity. Moments of inertia, kinetic energy, and angular momentum of a rigid body with axial symmetry. Gyroscopes and the classical integrable cases of rigid body motion.

1. N. M. J. Woodhouse, Introduction to Analytical Mechanics (1987). Chapters 3 and 6. (This is out of print, but still available in most College libraries.)

Further Reading

1. M. Lunn, A First Course in Mechanics (OUP, 1991). Chapters 6, 7.2, 7.3, 8.3 and 8.4.