PHYS456-21S1 (C) Semester One 2021

Classical Mechanics

15 points

Details:
Start Date: Monday, 22 February 2021
End Date: Sunday, 27 June 2021
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Sunday, 7 March 2021
  • Without academic penalty (including no fee refund): Friday, 14 May 2021

Description

Classical Mechanics

Learning Outcomes

In this course students will embark on a voyage of discovery of the deep theoretical principles
that underlie Newtonian and relativistic mechanics, and to appreciate why the laws
of physics are the way they are. They will learn new ways of thinking about the physical
world which allow deeper appreciation of the links between the classical and quantum
regimes.

Armed with the powerful techniques of Lagrangian and Hamiltonian dynamics, and Cartesian
tensors, students will have the tools to simplify complex mechanical problems to their
basic elements. With elegant symmetry principles such as Noether’s theorem they will
understand the deep connection between symmetries of spacetime and conservation laws,
seeing how, for example, Kepler’s second law follows from rotational symmetry and conservation
of angular momentum. They will apply this new understanding to a variety of
physical systems, from coupled oscillators to particles moving in electromagnetic fields.
Finally they will discover how the symmetries of special relativity are most succinctly described
with the language of 4-vectors, and derive the Lorentz group from the Principle of
Relativity.

This course is the basis for all advanced courses in theoretical physics.

OUTLINE
* Dynamical systems – definitions. Constrained systems. Lagrange’s equations.
* Principle of least action. Euler-Lagrange equations.
* Symmetries, conservation laws and Lie groups. Noether’s theorem.
* Oscillations: linearization. The linear chain.
* Hamiltonian formulation. Legendre’s transformation.
* Transformation theory. Canonical transformations. Generating functions. Poisson
brackets.
* Hamilton-Jacobi method. Physical applications: (e.g. wave mechanics and Schr¨odinger’s
equation).
* Special relativity: Kinematics, symmetries and Lagrangian formulation

Pre-requisites

Subject to approval of the Head of Department.

Timetable 2021

Students must attend one activity from each section.

Lecture A
Activity Day Time Location Weeks
01 Tuesday 09:00 - 10:00 F3 Lecture Theatre
22 Feb - 4 Apr
26 Apr - 6 Jun
Lecture B
Activity Day Time Location Weeks
01 Wednesday 09:00 - 10:00 Ernest Rutherford 140
22 Feb - 4 Apr
26 Apr - 6 Jun
Drop in Class A
Activity Day Time Location Weeks
01 Monday 12:00 - 13:00 Jack Erskine 111
3 May - 9 May
Drop in Class B
Activity Day Time Location Weeks
01 Friday 11:00 - 13:00 Jack Erskine 244
7 Jun - 13 Jun
Tutorial A
Activity Day Time Location Weeks
01 Friday 10:00 - 11:00 F1 Lectorial
22 Feb - 28 Mar
26 Apr - 6 Jun

Examination and Formal Tests

Test A
Activity Day Time Location Weeks
01 Monday 18:30 - 19:30 Beatrice Tinsley 111
3 May - 9 May

Course Coordinator / Lecturer

David Wiltshire

Assessment

Assessment Due Date Percentage  Description
Final Exam 60%
Homework 20% Five problem sets, best four out of five count.
Presentation 10% Students are required to give a 15 minute lecture on the topic of Classical Chaos.
Term Test 10%

Textbooks / Resources

Additional reading

D.E. Bourne and P.C. Kendall, Vector Analysis and Cartesian Tensors, (Thomas Nelson
& Sons, Sunbury-On-Thames UK, 1977), chapter 8, [for Orthogonal Transformations in
§3 only].

D.W. Jordan and P. Smith, Nonlinear Ordinary Differential Equations, 3rd ed. (Oxford
University Press, 1999) chapters 1,2 [for §4. Oscillations only]

N.A. Doughty, Lagrangian Interaction, (Addison Wesley, Sydney, 1990), chapters 12,13
[for §6. Special Relativity only].

Additional Course Outline Information

Academic integrity

Indicative Fees

Domestic fee $1,066.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see School of Physical & Chemical Sciences on the department and colleges page .

All PHYS456 Occurrences

  • PHYS456-21S1 (C) Semester One 2021