Course Catalogue

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This course introduces students to a geometric view of classical mechanics which draws together many problems in the constrained and unconstrained motions of systems of particles and continua as well as providing the underlying framework for modern quantum mechanics.

17 x 1 hr lectures and 6 x 1 hr tutorials in a semester

Mandatory Entry Requirements

3H: Mathematical Methods (MATHS4075)
3H: Mechanics of Rigid and Deformable Bodies (MATHS4078)

Recommended Entry Requirements

Assessment

90% Examination, 10% Coursework.

Reassessment

In accordance with the University's Code of Assessment reassessments are normally set for all courses which do not contribute to the honours classifications. For non honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students, and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions are listed below in this box.

Reassessments are normally available for all courses, except those which contribute to the Honours classification. For non Honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions for this course are described below. 

The main aim of this course is the study of the dynamical properties of systems consequent upon specific choices of Hamiltonian function. It will develop the theory from the Lagrangian approach familiar from previous courses, introducing the structures of symplectic geometry associated with phase spaces of particulate and rigid body motions. Hamiltonian symmetries will play a crucial role in the explicit description of the associated spaces of orbits. It will conclude with a discussion of some basic notoins of Quantum Mechanics. 

By the end of this course students will be able to:

(a) Move seamlessly between the Lagrangian and Hamiltonian formulations of a given mechanical or optical system;

(b) Given an appropriate geometric situation, describe the associated Hamiltonian;

(c) Identify and employ integrals of motion arising from symmetries to reduce the order of a system;

(d) Implement symplectic transformations between equivalent Hamiltonian systems;

(e) Discuss separable coordinates in appropriate situations;

(f) Present treatments of very simple quantised systems.

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.