Dynamics, Chaos & Special Relativity
University of Queensland
Area of Study
Taught In English
MATH1052 + PHYS1001 + PHYS1002
Course Level Recommendations
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Host University Units2
Recommended U.S. Semester Credits4
Recommended U.S. Quarter Units6
Hours & Credits
OverviewCourse DescriptionIntroduction to Lagrangian & Hamiltonian mechanics including elementary treatment of chaos in Hamiltonian systems. Calculus of variations, constraints, generalised coordinates, geometrical methods. Introduction to Special Relativity including relativistic particle mechanics.Course IntroductionWhat is exciting about classical mechanics? Wasn't it all done years ago by Newton, and encapsulated in three laws? No! Classical mechanics is surprisingly rich, encompassing such behaviour as chaos, nonlinear resonances and transitions to chaos. The principle of stationary action leads to the powerful formulation of Lagrangian and Hamiltonian mechanics, which highlights the role of symmetry and conservation laws. Much of this formulation survives into quantum mechanics.Chaotic dynamics had been known to exist for a long time, but it was not until the 1970's and 1980's that its importance in a wide variety of applications began to be appreciated. In reality, chaos is ubiquitous. This course introduces deterministic chaos in nonlinear classical systems, where the dynamics is deterministic yet inherently unpredictable.Finally, this course provides further development of the subject of special relativity that was introduced at first year, providing an introduction to four vector notation, relativistic particle mechanics and elementary space-time physics.Learning ObjectivesAfter successfully completing this course you should be able to:
Class Contact4 Contact hoursAssessment SummaryProblem Sets
- Solve elementary mechanical problems using the Lagrangian and Hamiltonian formalisms.
- Solve basic problems in the calculus of variations.
- Draw phase-space portraits of elementary dynamical systems and identify the various features.
- Understand what is meant by "chaotic dynamics" in terms of sensitive dependence on initial conditions.
- Understand how chaos arises in non-linear Hamiltonian systems, and be able to determine which initial conditions lead to chaos for driven systems with one degree of freedom.
- Understand the principles of special relativity.
- Understand four vectors and use them to solve simple relativistic mechanical problems.
- Problem Set(s) - Special Relativity: 9%
- Problem Set(s) - Lagrangian dynamics: 15%
- Progleb Set(s) - Hamiltonial dynamics and chaos: 12%
- Mid-Semester: 16%
- Final: 48%
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Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.