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The aim of the course is to give a complete understanding of Classical Mechanics at an advanced level. The course provides indispensable preparation for all advanced courses in theoretical physics. Techniques learned have wide use in advanced quantum mechanics, classical and quantum field theory, general relativity, particle physics and statistical mechanics.
Content:
1) Lagrangian Formulation of Mechanics: Calculus of Variations, Action Integral, Principle of Least Action, Euler-Lagrange Equation, Generalized Co-ordinates and Momenta, Constraints, Normal Modes, Conservation Laws: energy, linear momentum, angular momentum. Integration of the equations of movement: problems with one degree of freedom, two body problem, movement in a central field, scattering in a central field
2) Hamiltonian Formulation of Mechanics: Hamilton’s Equations, Poisson Brackets, Canonical Transformations, Liouville theorem, adiabatic invariants
3) Continuous Symmetries and Conservations Laws.
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