PHYS456-23S1 (C) Semester One 2023

# Classical Mechanics

15 points

Details:
 Start Date: Monday, 20 February 2023 End Date: Sunday, 25 June 2023
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Sunday, 5 March 2023
• Without academic penalty (including no fee refund): Sunday, 14 May 2023

## 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

## Prerequisites

Subject to approval of the Head of Department.

## Timetable 2023

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01-P1 Monday 09:00 - 10:00 Link 309 Lecture Theatre 20 Feb - 2 Apr 01-P2 Monday 17:00 - 18:00 Jack Erskine 446 24 Apr - 4 Jun Lecture B 01-P1 Tuesday 09:00 - 10:00 Rehua 002 Lectorial 20 Feb - 26 Mar 01-P2 Tuesday 17:00 - 18:00 Rehua 002 Lectorial 24 Apr - 4 Jun Lecture C 01 Thursday 13:00 - 14:00 Ernest Rutherford 465 27 Mar - 2 Apr Drop in Class A 01 Thursday 13:00 - 14:00 Ernest Rutherford 465 20 Feb - 26 Mar 24 Apr - 4 Jun Lecture A 01 Tuesday 08:30 - 10:00 Rehua 002 Lectorial 27 Mar - 2 Apr Tutorial A 01 Wednesday 17:00 - 18:00 Ernest Rutherford 465 20 Feb - 2 Apr 24 Apr - 4 Jun

## 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% Tuesday, 2nd April - 3:00 - 3:55pm

## Textbooks / Resources

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].