PHYSICS 7032 - Advanced Dynamics and Relativity

North Terrace Campus - Semester 2 - 2019

This course will give students a working knowledge of analytical mechanics and relativity to the standard required for further study in physics. Mechanics: Lagrangian mechanics, variational techniques, conservation laws, Noether's theorem, small oscillations, Hamiltonian mechanics, Poisson brackets. Relativity: space-time vectors and tensors, relativistic mechanics, electrodynamics, field-strength tensor, Lienard-Wiechert potentials.

  • General Course Information
    Course Details
    Course Code PHYSICS 7032
    Course Advanced Dynamics and Relativity
    Coordinating Unit School of Physical Sciences
    Term Semester 2
    Level Postgraduate Coursework
    Location/s North Terrace Campus
    Units 3
    Contact Up to 4 hours per week
    Available for Study Abroad and Exchange Y
    Prerequisites PHYSICS 2532, PHYSICS 2534, MATHS 2101 or MATHS 2201, MATHS 2102 or MATHS 2202
    Incompatible PHYSICS 3006
    Assessment Assignment, written exam
    Course Staff

    Course Coordinator: Associate Professor Ross Young

    Course Timetable

    The full timetable of all activities for this course can be accessed from Course Planner.

  • Learning Outcomes
    Course Learning Outcomes

    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 and communicate appropriate techniques for solving a range of problems;

    9. apply appropriate techniques to develop a solution; and

    10. assess and communicate the validity of assumptions made, and the correctness of the solution.
    University Graduate Attributes

    This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:

    University Graduate Attribute Course Learning Outcome(s)
    Deep discipline knowledge
    • informed and infused by cutting edge research, scaffolded throughout their program of studies
    • acquired from personal interaction with research active educators, from year 1
    • accredited or validated against national or international standards (for relevant programs)
    Critical thinking and problem solving
    • steeped in research methods and rigor
    • based on empirical evidence and the scientific approach to knowledge development
    • demonstrated through appropriate and relevant assessment
    Teamwork and communication skills
    • developed from, with, and via the SGDE
    • honed through assessment and practice throughout the program of studies
    • encouraged and valued in all aspects of learning
  • Learning Resources
    Required Resources

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

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

    Online Learning
    MyUni: Teaching materials and course documentation will be posted on the MyUni website (
  • Learning & Teaching Activities
    Learning & Teaching Modes

    - 3 Lectures of 1 hour each per week

    - 1 Tutorial of 1 hour per week

    The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

    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).
    Learning Activities Summary

    Ø 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.

    Ø 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.

    Ø Oscillations (10%)
    - General definitions of equilibrium and stability, small oscillations about equilibrium, normal coordinates, coupled pendula, linear chain (1-D crystal).

    Ø 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.

    Ø 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.

    Ø 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.

    Ø 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
    Specific Course Requirements

  • Assessment

    The University's policy on Assessment for Coursework Programs is based on the following four principles:

    1. Assessment must encourage and reinforce learning.
    2. Assessment must enable robust and fair judgements about student performance.
    3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
    4. Assessment must maintain academic standards.

    Assessment Summary
    Assessment task Type of assessment Percentage of total assessment

    Yes or No #
    Objectives being assessed / achieved
    Assignments & Tests Formative & Summative 30% - 40% No 1 – 10
    Exam Summative 60% - 70% No 1 – 10
    Assessment Related Requirements

    Assessment Detail

    While this course is offered concurrently to undergraduate students, all postgraduate students are expected to perform at a higher level both qualitatively and quantitatively. To facilitate this, postgraduate students are required to address additional content in the projects and the examination within the same timeframe as undergraduate students.

    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.

    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 supplementary 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.
    Course Grading

    Grades for your performance in this course will be awarded in accordance with the following scheme:

    M10 (Coursework Mark Scheme)
    Grade Mark Description
    FNS   Fail No Submission
    F 1-49 Fail
    P 50-64 Pass
    C 65-74 Credit
    D 75-84 Distinction
    HD 85-100 High Distinction
    CN   Continuing
    NFE   No Formal Examination
    RP   Result Pending

    Further details of the grades/results can be obtained from Examinations.

    Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.

    Final results for this course will be made available through Access Adelaide.

  • Student Feedback

    The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.

    SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy ( course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.

  • Student Support
  • Policies & Guidelines
  • Fraud Awareness

    Students are reminded that in order to maintain the academic integrity of all programs and courses, the university has a zero-tolerance approach to students offering money or significant value goods or services to any staff member who is involved in their teaching or assessment. Students offering lecturers or tutors or professional staff anything more than a small token of appreciation is totally unacceptable, in any circumstances. Staff members are obliged to report all such incidents to their supervisor/manager, who will refer them for action under the university's student’s disciplinary procedures.

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