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MC256 Lagrangian and Hamiltonian Dynamics

MC256 Lagrangian and Hamiltonian Dynamics

Credits: 10 Convenor: Dr. M. D. Dampier Semester: 2
Prerequisites: essential: MC123, MC126, MC127, MC224
Assessment: Regular coursework: 20% One and a half hour exam in May/June: 80%
Lectures: 18 Problem Classes: 5
Tutorials: none Private Study: 52
Labs: none Seminars: none
Project: none Other: none
Surgeries: none Total: 75

Course Description

This course is an introduction to the classical Lagrangian and Hamiltonian methods of analytical dynamics.

Aims

To introduce the powerful methods of analytical dynamics, and to apply the theory to some important physical problems. The selection of topics chosen will provide a foundation for further study, and be sufficient for the solution of most problems in dynamics that the student will encounter elsewhere in the degree.

Objectives

Syllabus

  1. Dynamics in 1-dimension, the energy diagram.
  2. Dynamics in 3-dimensions, coordinates, constraints.
  3. Lagrange's equations.
  4. Symmetries and conserved quantities.
  5. Orbits, oscillations.
  6. Hamilton's equations, phase space.
  7. Poisson brackets and integrals.

Transferable Skills

Most of the methods used in this module - qualitative approaches to a problem, setting up the differential equations appropriate to a physical situation, reducing the complexity of a system of differential equations by using known first integrals, and the geometric representation of problems - will be found widely applicable in other areas of applied and industrial mathematics.

Reading list

N.M.J.Woodhouse, Introduction to Analytical Dynamics, Clarendon Press, Oxford, 1987.

Details of Assessment

The final assessment of this module will consist of 20% coursework and 80% from the one and a half hour examination in May/June. The coursework contribution will come from weekly work. The examination paper will contain 4 questions with full marks obtainable for solutions to any 3.

Next: MC262 Linear Regression Models Up: Year 2 Previous: MC255 Algebra II

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Last updated: 2001-09-20
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