Lagrangian & Hamiltonian Dynamics (Adv) (MATH3977)

UNIT OF STUDY

This unit provides a comprehensive treatment of dynamical systems using the mathematically sophisticated framework of Lagrange and Hamilton. This formulation of classical mechanics generalizes elegantly to modern theories of relativity and quantum mechanics. The unit develops dynamical theory from the Principle of Least Action using the calculus of variations. Emphasis is placed on the relation between the symmetry and invariance properties of the Lagrangian and Hamiltonian functions and conservation laws. Coordinate and canonical transformations are introduced to make apparently complicated dynamical problems appear very simple. The unit will also explore connections between geometry and different physical theories beyond classical mechanics. Students will be expected to solve fully dynamical systems of some complexity including planetary motion and to investigate stability using perturbation analysis. Hamilton-Jacobi theory will be used to elegantly solve problems ranging from geodesics (shortest path between two points) on curved surfaces to relativistic motion in the vicinity of black holes. This unit is a useful preparation for units in dynamical systems and chaos, and complements units in differential equations, quantum theory and general relativity.

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Further unit of study information

Classes

Three 1 hour lectures and one 1 hour tutorial per week.

Assessment

One 2 hour exam and assignments and/or quizzes (100%)

Faculty/department permission required?

No

Unit of study rules

Prerequisites and assumed knowledge

12 credit points of Intermediate Mathematics with at least Credit average

Prohibitions

MATH2004, MATH3917, MATH2904

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