Hamiltonian Dynamics (U01431)

? Credit Points : 10 ? SCQF Level : 11 ? Acronym : PHY-4-HamDyn

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, canonical transformations and Hamilton-Jacobi theory, action-angle variables, autonomous systems, canonical perturbation theory. Introduction to continuous systems.

Entry Requirements

? Pre-requisites : At least 80 credit points accrued in courses of SCQF Level 9 or 10 drawn from Schedule Q, including Lagrangian Dynamics (PHY-3-LagDyn); Tensors & Fields (PHY-3-TensFlds) is desirable.

Subject Areas

Home subject area

Undergraduate (School of Physics), (School of Physics, Schedule Q)

Delivery Information

? Normal year taken : 4th year

? Delivery Period : Semester 1 (Blocks 1-2)

? Contact Teaching Time : 2 hour(s) per week for 11 weeks

First Class Information

Date	Start	End	Room	Area	Additional Information
21/09/2006	15:00	16:00	Lecture Room 6206, JCMB	KB

All of the following classes

Type	Day	Start	End	Area
Lecture	Monday	15:00	15:50	KB
Lecture	Thursday	15:00	15:50	KB

? Additional Class Information : Workshop/tutorial sessions, as arranged.

Summary of Intended Learning Outcomes

Upon successful completion of this course it is intended that a student will be able to:
1)know how to derive Hamiltonians for simple mechanical systems and to appreciate the power of the variational approach for deriving the equations of motion without needing vectors of the Newtonian approach;
2)be familiar with the concept of phase space for describing the motion of time dependent systems;
3)understand the significance of canonical transformations, in particular leading to the Hamilton-Jacobi equation and to the advantages of using action-angle variables;
4)be familiar with the behaviour of one and two dimensional autonomous systems near fixed points;
5)appreciate the difference between integrable and non-integrable systems;
6)understand the method of canonical perturbation theory;
7)have a deeper insight into the structure of classical mechanics;
8)to be able to apply what has been learnt in the course to solving new problems.