Courses Catalogue

Advanced Classical Mechanics And Special Relativity

COURSE CODE: PHY7109
COURSE CREDIT UNIT: 4
ACADEMIC PROGRAMME: Physics, M.Sc
COLLEGE/SCHOOL/FACULTY: School of Natural and Applied Sciences
STATUS: Core
PROGRAMME TYPE: Postgraduate

Course Description

A review of the basic principles and introduction to advanced methods of mechanics, emphasizing the relationship between dynamical symmetries and conserved quantities, as well as classical mechanics as a background to quantum mechanics. The course presents kinematics and dynamics of particles using Newtonian, Langrangian and Hamiltonian techniques. Topics include Lagrangian and Hamiltonian Formulations, Mechanics of Rigid Bodies, Canonical Transformation, Small Oscillations and Relativity.

COURSE JUSTIFICATION/RATIONALE

To provide a working knowledge of analytical mechanics and relativity to the standard required for further study in physics.

LEARNING OBJECTIVES

By the end of this course, the student should be able to:

  • Discuss Newtonian mechanics (survey of undergraduate mechanics) with forces and torques to solve problems in Cartesian and curvilinear coordinates. Solve mechanics problems using work-energy, and conservation of energy, momentum and angular momentum.
  • Analyse rigid-body problems at the level of Goldstein and similar texts.
  • Solve mechanics problems in non-inertial frames.
  • Explain Lagrangian mechanics to obtain the equations of motion for a variety of problems, including the use of generalized coordinates and cyclic coordinates.
  • Examine perturbation and similar techniques to linearize equations of motion to analyze stability and study coupled systems using normal modes. Discuss the Lorentz transformation equations.

By the end of this course, the student should be able to:

  • Discuss Newtonian mechanics (survey of undergraduate mechanics) with forces and torques to solve problems in Cartesian and curvilinear coordinates.
  • Solve mechanics problems using work-energy, and conservation of energy, momentum and angular momentum.
  • Analyse rigid-body problems at the level of Goldstein and similar texts.
  • Solve mechanics problems in non-inertial frames.
  • Explain Lagrangian mechanics to obtain the equations of motion for a variety of problems, including the use of generalized coordinates and cyclic coordinates.
  • Examine perturbation and similar techniques to linearize equations of motion to analyze stability and study coupled systems using normal modes.
  • Discuss the Lorentz transformation equations.

 LEARNING OUTCOMES

A student completing the course is expected to demonstrate knowledge and understanding of:

  • Lagrangian methods for problem solving, including small oscillations;
  • the relation between symmetry and conservation;
  • the Hamiltonian formulation and its connection with quantum mechanics;
  • the space-time approach to relativity and four-vectors;
  • relativistic kinematics and optics;
  • relativistic analytic mechanics for a particle coupled to a field;
  • co-variant form of Maxwell's electromagnetic equations;
  • techniques for solving a range of problems;
  • techniques to develop a solution; and validity of any assumptions that were made, and the correctness of the solution.