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, the
symplectic structure of classical mechanics,
canonical transformations and Hamilton-Jacobi theory, action-angle variables and an 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 2 (Blocks 3-4)

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

First Class Information

Date	Start	End	Room	Area	Additional Information
08/01/2008	11:00	12:00	Lecture Room 6206, JCMB	KB

All of the following classes

Type	Day	Start	End	Area
Lecture	Tuesday	11:10	12:00	KB
Lecture	Friday	11:10	12:00	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;
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 dynamical systems near fixed points;
5)appreciate the difference between integrable and non-integrable systems;
6)have a deeper insight into the (symplectic) structure of classical mechanics and its formal connection to quantum mechanics;
7)to be able to apply what has been learnt in the course to solving new problems.