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Semester 2

Hamiltonian Dynamics (PHYS11012)

Course Website

http://www2.ph.ed.ac.uk/~rhorsley/

Subject

Physics and Astronomy

College

SCE

Credits

10

Normal Year Taken

4

Delivery Session Year

2023/2024

Pre-requisites

Course Summary

This course assumes a knowledge of Lagrangian dynamics. The main topics covered are: the Hamiltonian formulation for systems with a finite number of degrees of freedom, the symplectic structure of classical mechanics,canonical transformations and Hamilton-Jacobi theory, action-angle variables and an introduction to continuous systems.

Course Description

Review of Lagrangian dynamics, generalised coordinates, symmetries and Noether's theoremHamilton's equations, conservative systems, phase space and Liouville's TheoremCanonical Transformations, generating functions, Poisson bracketsQualitative dynamics, behaviour of low dimensional autonomous systems, fixed points and limit cycles, simple preditor--prey systemsHamilton-Jacobi equation, principal and characteristic functions, separation of variables, connection with quantum mechanicsAction-Angle variables, integrability, libration and rotation, the Kepler problemCanonical Perturbation theory (both time independent and time dependent) adiabatic invariants, the KAM theorem (descriptive)

Assessment Information

Written Exam 100%, Coursework 0%, Practical Exam 0%

Additional Assessment Information

Degree Examination, 100%

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