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Module MA2341: Advanced Classical Mechanics I

Credit weighting (ECTS)
5 credits
Semester/term taught
Michaelmas term 2018-19
Contact Hours
11 weeks, 3 lectures including tutorials per week
 
Lecturer
Prof Sergey Frolov
 
Learning Outcomes
On successful completion of this course, students will (be able to):
  • have a knowledge of the Lagrangian mechanics including a familiarity with Lagrangians describing various important mechanic systems;
  • derive the equations of motion of a mechanical system with several degrees of freedom from its Lagrangian by using Hamilton’s principle;
  • use Noether’s theorem to derive conservation laws;
  • analyse qualitatively and quantitatively the motion of one-dimensional systems and in a central field;
  • analyse small free oscillations, forced oscillations and damped oscillations of a system with any number of degrees of freedom, compute its characteristic frequencies and normal coordinates;
  • use Euler angles and Euler equations to analyze the motion of a rigid body;

Module Content
  • Lagrangian, Hamilton’s principle, Lagrange's equations, Constrained dynamics;
  • Conservation laws and Noether’s theorem ;
  • Motion in one dimension and central potential;
  • Oscillations: Equilibrium and motion near equilibrium;
  • Rigid body motion, Euler equations;

Module Prerequisite
MA1241 - Mechanics I

Recommended Reading
  • Herbert Goldstein, Classical Mechanics, third edition, Addison Wesley
  • V.I. Arnold, Mathematical Methods of Classical Mechanics, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • S. Thornton, J.Marion, 'Classical Dynamics of Particles and Systems', 5th Edition, Brooks/Cole 2004
Relativity
  • L.D. Landau and E.M. Lifshitz, The Classical Theory of Fields: Volume 2 (Course of Theoretical Physics Series), Butterworth-Heinemann
 
Required Reading
  • L.D. Landau and E.M. Lifshitz, Mechanics, Butterworth-Heinemann

Assessment Detail

This module will be examined jointly in a 2-hour examination in Michaelmas term. Continuous assessment will contribute 20% to the final grade for the module at the annual examination session.