Synopsis for Dynamics

Overview

The subject of dynamics is about how things change with time. A major theme is the modelling of a physical system by differential equations, and one of the highlights involves using the law of gravitation to account for the motion of planets.

Learning Outcomes

Students will be familiar with the laws of motion, including circular and planetary motion. They will know how forces are used and be introduced to stability and chaos in a physical system.

Synopsis

Newton's laws [in 3 dimensions, including angular momentum and torque for systems of particles]. Free and forced linear oscillations. Simple oscillatory systems with two degrees of freedom, natural frequencies.

Two dimensional motion. Use of polar coordinates, circular motion. [Angular velocity, Coriolis formula (i.e. )] Central forces, differential equation for the particle path. Inverse square law, planetary orbits. Energy and potential for one dimensional motion.

Equivalent ideas for central force problems and three dimensional problems with axial symmetry.

Axisymmetric rigid bodies/moments of inertia; precession of Lagrange top by vector methods.

Examples of stability and instability in physical situations, via linearised equations.

Reading

1. David Acheson, From Calculus to Chaos: an Introduction to Dynamics (Oxford University Press, 1997), Chapters 1, 5, 6, 10, 11.

Further Reading

1. M. W. McCall, Classical Mechanics: A Modern Introduction (Wiley, 2001), Chapters 1–4, 7.
2. M. Lunn, A First Course in Mechanics (Oxford University Press, 1991), Chapters 1–3 (up to 3.4).