1. To provide students with an awareness of the physical principles that can be applied to understand important features of classical (i.e. non-quantum) mechanical systems.
2. To provide students with techniques that can be applied to derive and solve the equations of motion for various types of classical mechanical systems, including systems of particles and fields.
3. To develop students'' understanding of the fundamental relationship between symmetries and conserved quantities in physics.
   
4. To reinforce students’ knowledge of quantum mechanics, by developing and exploring the application of closely-related concepts in classical mechanics.

Students should know the physical principles underlying the Lagrangian and Hamiltonian formulations of classical mechanics, in particular D’Alembert’s principle and Hamilton’s principle, and should be able to explain the significance of these advanced principles in classical and modern physics.

Students should be able to apply the Euler-Lagrange equations and Hamilton’s equations (as appropriate) to derive the equations of motion for specific dynamical systems, including complex nonlinear systems.

Students should be able to use advanced concepts in classical mechanics to describe the connection between symmetries and conservation laws.

Students should be able to apply advanced techniques, including conservation laws, canonical transformations, generating functions, perturbation theory etc. to describe important features of various dynamical systems (including systems of particles and fields) and to solve the equations of motion in specific cases.

1. Lagrangian mechanics
• Lagrange’s equations derived from D’Alembert’s principle
• Lagrange’s equations derived from Hamilton’s principle
• Examples of the application of Lagrange’s equations in mechanical systems
2. Hamiltonian mechanics
• Conjugate momenta 
• From the Lagrangian to the Hamiltonian
• Derivation of Hamilton’s equations
• Examples of the application of Hamilton’s equations in mechanical systems
3. Charged particle in an electromagnetic field
• Lagrangian for a charged particle in an EM field
• Hamiltonian for a charged particle in an EM field
• Relativistic form of the Hamiltonian
4. Symmetries and conservation laws
• Cyclic variables
• Continuous symmetries and invariants;  Noether’s theorem
• Canonical invariants
• Poisson brackets
• Symplecticity;  Liouville’s theorem
5. Canonical transformations
• Mixed-variable generating functions
• The Hamilton-Jacobi equation
• Action-angle variables
• Examples of application of canonical transformations
6. Continuous systems (field theory)
• Derivation of field equations
• Symmetries, conservation laws and Noether’s theorem for fields

Lecture - The course material will be delivered in a series of 36×1-hour lectures.

36 x 1 hour lectures

Tutorial - 6 x 1 hour tutorials/problem classes: during the tutorials/problem classes, students will work through set problems, with assistance (as needed) from lecturers/demonstrators.

Key Text
H. Goldstein, C.P. Poole Jr, J.L. Safko, “Classical Mechanics” (Pearson, 3^rd Edition, 2013)

Recommended Text
P. Hamill, “A Student’s Guide to Lagrangians and Hamiltonians” (Cambridge University Press, 2013)