PHYS326-24S1 (C) Semester One 2024

# Classical Mechanics and Symmetry Principles

15 points

Details:
 Start Date: Monday, 19 February 2024 End Date: Sunday, 23 June 2024
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Sunday, 3 March 2024
• Without academic penalty (including no fee refund): Sunday, 12 May 2024

## Description

The Lagrangian and Hamiltonian formulations of classical mechanics which provide essential preparation for all advanced courses in theoretical physics. Techniques learned have wide use in advanced quantum mechanics, quantum field theory, general relatively, particle physics and statistical 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

## Prerequisites

(1) PHYS202 or PHYS205; (2) PHYS203; (3) MATH201 RP: MATH202 and MATH203

## Timetable 2024

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Monday 14:00 - 15:00 E16 Lecture Theatre 19 Feb - 31 Mar 22 Apr - 2 Jun Lecture B 01 Tuesday 13:00 - 14:00 E16 Lecture Theatre 19 Feb - 31 Mar 22 Apr - 2 Jun Drop in Class A 01 Monday 16:00 - 17:00 Ernest Rutherford 225 26 Feb - 31 Mar 6 May - 2 Jun Drop in Class B 01 Thursday 11:00 - 12:00 Ernest Rutherford 260 4 Mar - 10 Mar 18 Mar - 24 Mar 29 Apr - 5 May 13 May - 19 May 27 May - 2 Jun Drop in Class C 01 Friday 12:00 - 13:00 Rehua 003 Music 22 Apr - 28 Apr Drop in Class D 01 Thursday 16:00 - 17:00 Rehua 103 Project Workshop 3 Jun - 9 Jun Drop in Class E 01 Friday 13:00 - 14:00 Rehua 003 Music 3 Jun - 9 Jun Tutorial A 01 Thursday 16:00 - 17:00 Ernest Rutherford 465 19 Feb - 31 Mar 6 May - 2 Jun Tutorial B 01 Monday 16:00 - 17:00 Jack Erskine 111 22 Apr - 5 May

## Examinations, Quizzes and Formal Tests

Activity Day Time Location Weeks Test A 01 Friday 16:00 - 17:30 Jack Erskine 031 Lecture Theatre 22 Apr - 28 Apr

## Assessment

Assessment Due Date Percentage  Description
Final Exam 65%
Problem Sets 20% The best 4 out of 5 willl count.
Test 15%

## Textbooks / Resources

#### Required Texts

Goldstein, Herbert , Poole, Charles P., Safko, John L; Classical mechanics ; 3rd ed; Addison Wesley, 2002.

Arnold, V. I; Mathematical methods of classical mechanics ; 2nd ed.; Springer-Verlag, 1989.

I. Percival and D. Richards,; Introduction to Dynamics ; Cambridge University Press, 1982.

L. Landau and E. Lifschitz,; Mechanics ; 3rd Edition; Pergamon, 1976.

Saletan, Eugene J. , Cromer, Alan H; Theoretical mechanics ; Wiley, 1971.

T.L. Chow; Classical Mechanics ; Wiley, New York,, 1995.

D.E. Bourne and P.C. Kendall, Vector Analysis and Cartesian Tensors, 3rd ed, (CRC Press 2002), chapter 8, [for Orthogonal Transformations in §3 only].

D.W. Jordan and P. Smith, Nonlinear Ordinary Differential Equations, 4th ed. (Oxford
University Press, 2007) chapters 1,2 [for §4. Oscillations only]

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

## Indicative Fees

Domestic fee \$978.00

International fee \$4,988.00

* 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 .

## All PHYS326 Occurrences

• PHYS326-24S1 (C) Semester One 2024