This module introduces the learner to a selection of standard introductory topics in classical mechanics. General strategies for problem solving are discussed. The learner will encounter the Newtonian, Lagrangian and Hamiltonian formulations of classical mechanics and develop an understanding of the relationships between these approaches. Numerical simulations are used to develop physical intuition of selected problems.
Statics
Forces; torques; static balance problems.
Newtonian mechanics
Newton’s laws; free-body diagrams; polar and Cartesian coordinate systems; simple, damped, driven, and coupled harmonic motion; solving ODEs arising from Newton’s laws; numerical simulation
Conservation laws
Kinetic and potential energy; conservation of energy; work-energy theorem; conservation of momentum; change of reference frame (centre of mass); elastic and inelastic collisions, central forces.
Lagrangian mechanics
Euler-Lagrange equations; principle of least action; constraining forces; generalised and ignorable coordinates; Noether’s theorem and conservation laws; small oscillations
Hamiltonian Mechanics
Energy and the Hamiltonian; Hamilton’s equations; Legendre transforms; Liouville’s theorem
Lectures supported by tutorials
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Formal Examination | 70 |
| Other Assessment(s) | 30 |