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1. explain Lagrangian methods for problem solving, including small oscillations;
2. explain the relation between symmetry and conservation;
3. discuss the Hamiltonian formulation and its connection with quantum mechanics;
4. discuss the space-time approach to relativity and four-vectors;
5. explain relativistic kinematics and optics;
6. discuss relativistic analytic mechanics for a particle coupled to a field;
7. discuss covariant form of Maxwell's electromagnetic equations;
8. recognise appropriate techniques for solving a range of problems;
9. apply appropriate techniques to develop a solution; and
10. assess the validity of any assumptions that were made, and the correctness of the solution.

Goldstein, H., C. Poole and J. Savko, Classical Mechanics 3rd ed., Addison-Wesley, 2002.

Rindler, W., Introduction to Special Relativity, 2nd ed., OUP 1991

MyUni:    Teaching materials and course documentation will be posted on the MyUni website ().

This course will be delivered by the following means:

-         3 Lectures of 1 hour each per week

-         1 Tutorial of 1 hour per week

A student enrolled in a 3 unit course, such as this, should expect to spend, on average 12 hours per week on the studies required. This includes both the formal contact time required to the course (e.g., lectures and practicals), as well as non-contact time (e.g., reading and revision).

Coursework Content

• Lagrangian Mechanics (27%)

-           Newton's Laws for multiparticle systems; role of Third Law, breakdown for velocity-dependent Lorentz force.

-           Constrained systems, rigid body, Euler angles; holonomic constraints, generalized coordinates, velocity dependent constraints, e.g. not integrable for rolling sphere.

-           D'Alembert's principle, generalised velocity and force, conservative force, Lagrangian and equations of motion, velocity-dependent potentials, equivalent Lagrangians.

-           Lagrangian calculations: plane pendulum, central force field (orbits & scattering), rigid body systems (CM translation plus rotation about CM).

-           Calculus of variations, functional derivative, connection with Euler-Lagrange equations, brachistochrone, catenary, Hamilton's action principle.

• Symmetries and Conservation Laws (10%)

-           Constants of integration, cyclic coordinates, generalised momentum.

-           Jacobi's first integral, relation to time translations and energy.

-           Noether's theorem for point mechanics, invariance under translations and rotations and conservation of momentum and angular momentum.

• Oscillations (10%)

-           General definitions of equilibrium and stability, small oscillations about equilibrium, normal coordinates, coupled pendula, linear chain (1-D crystal).

• Hamiltonian Mechanics (18%)

-           Legendre transforms (e.g. thermodynamics), phase space, Hamiltonian, Hamilton's equations, examples in Cartesian and polar coordinates, charged particle in electromagnetic fields.

-           Poisson brackets, PB form of Hamilton's equations, Jacobi identity, connection with quantum mechanics, relation to conserved quantities, Poisson bracket theorem.

-           Generalised phase-space coordinates, canonical transformations, invariance of PB's, preservation of Hamilton's equations, examples.

• Relativistic Kinematics (15%)

-           Inertial frames, Newton's First Law, Galilean space-time.

-           Einstein's axioms, space-time transformations, invariant interval, group of Lorentz transformations, metric tensor, space-/time-/light-like separations, rapidity, spacetime diagrams.

-           Time dilation, length contraction, velocity addition, Doppler effect, aberration, visual appearance of moving objects.

-           Four vectors, contravariance and covariance, tensors, covariance of physical equations, role of metric tensor.

• Relativistic Dynamics (8%)

-           Four-velocity, -acceleration, -force. Four-momentum and its conservation, particle collisions, CM and brick-wall frames, particle decay and scattering using fourvectors, flow of four-momentum in Feynman diagrams.

-           Action of a free relativistic particle, Hamiltonian, particle coupled to Lorentz scalar field.

• Electrodynamics (12%)

-           Four-potential, Lagrangian for charged particle in field, field-strength tensor and its dual, Lorentz force as four-vector, behaviour of E,B fields under boosts, field of uniformly moving charge.

• Covariant form of Maxwell's equations, conserved four-current, retarded Green's function, gauge choice, Liénard-Wiechert potentials

Assignments and Tests: (30% - 40% of total course grade)

The standard assessment consists of 2 projects and 2 tests/assignments. This may be varied by negotiation with students at the start of the semester. This combination of projects, tests and summative assignments is used during the semester to address understanding of and ability to use the course material and to provide students with a benchmark for their progress in the course.

Written Examination: (60% - 70% of total course grade)

One exam is given to address understanding of and ability to use the material.

Absence from Classes due to illness (or other valid reason)

If you miss a laboratory session or are unable to attend a tutorial due to illness (or any other valid reason) you will need to fill out a form within 3 working days of your missed session. All forms are available from the School Office or on MyUNI.

Submission of Assigned Work

Coversheets must be completed and attached to all submitted work. Coversheets can be obtained from the School Office (room G33 Physics) or from MyUNI. Work should be submitted via the assignment drop box at the School Office.

Extensions for Assessment Tasks

Extensions of deadlines for assessment tasks may be allowed for reasonable causes. Such situations would include compassionate and medical grounds of the severity that would justify the awarding of a replacement examination. Evidence for the grounds must be provided when an extension is requested. Students are required to apply for an extension to the Course Coordinator before the assessment task is due. Extensions will not be provided on the grounds of poor prioritising of time. The assessment extension application form can be obtained from:

Late submission of assessments

If an extension is not applied for, or not granted then a penalty for late submission will apply. A penalty of 10% of the value of the assignment for each calendar day that is late (i.e. weekends count as 2 days), up to a maximum of 50% of the available marks will be applied. This means that an assignment that is 5 days or more late without an approved extension can only receive a maximum of 50% of the mark.