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PX4517: ANALYTICAL MECHANICS AND ELEMENTS OF GENERAL RELATIVITY (2017-2018)

Last modified: 25 May 2018 11:16


Course Overview

Analytical mechanics, with its Lagrangian and Hamiltonian formulations, plays a pivotal role in almost every aspect of theoretical physics. It  highlights the role of conservation laws, the most fundamental laws of nature, in shaping the physical world in which we live.

Mastering Lagrangian and Hamiltonian mechanics allows one to better appreciate and understand cornerstone physical theories such as Quantum Mechanics or Statistical Mechanics.

As an alternative to Hamiltonian mechanics, in the second half of the course students may follow a 5 weeks elementary introduction to Einstein’s General relativity, the geometrical theory of gravitation, which generalizes special relativity and Newton’s gravitation.




Course Details

Study Type Undergraduate Level 4
Session Second Sub Session Credit Points 15 credits (7.5 ECTS credits)
Campus None. Sustained Study No
Co-ordinators
  • Professor Antonio Politi
  • Dr Charles Wang
  • Dr Silke Henkes

Qualification Prerequisites

  • Programme Level 4

What courses & programmes must have been taken before this course?

  • One of KL108W The Physical Universe A (Passed) or PX1014 The Physical Universe - 1 (Passed) or PX1015 The Physical Universe A (Passed) or PX1017 The Physical Universe a (Distance) (Passed) or PX2512 Cosmology, Astronomy and Modern Physics (Passed) or PX3011 Research Skills in Physics (Passed) or PX3015 Research and Computing Skills (Passed) or PX3017 Research and Computing Skills in Physics (Passed)
  • Either Mathematics (MA) (Studied) or Physics (PX) (Studied)
  • Any Undergraduate Programme (Studied)

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

None.

Are there a limited number of places available?

No

Course Description

Course Description

This course deals with analytical mechanics and general relativity, introducing fundamental theoretical concepts for applied mathematics and physics. 
Successful students will retain a comprehensive picture of classical mechanics and learn the basic concept of Lagrangian mechanics. Moreover, they will either learn the fundamental concepts of either Hamiltonian mechanics or General Relativity (see below).
All students are requested to follow part 1 of the course, while they are asked to choose between Part 2 (Hamiltonian formulation) and Part 3 (Introduction to General Relativity)

Part 1: Classical mechanics and its Lagrangian formulation (weeks 1-6).
The first part of the course offers a review of Newtonian mechanics, presented in a more formal framework which highlights conservations laws, introducing the Lagrangian formulation and discussing a number of physical applications.
Contents: Review of Newtonian mechanics; conservation laws; derivation of Kepler's laws of planetary motion; relative motion and Coriolis force; Foucault pendulum; Lagrangian formulation of mechanics; constrained systems; equilibrium solutions and their stability.

Part 2: Hamiltonian formulation (weeks 7-11)
The second part deals with Hamiltonian mechanics and a number of related theoretical concepts.
Contents: Hamiltonian formulation; canonical transformations;  action-angle coordinates and Hamilton Jacobi equations; Noether's theorem; Liouville theorem.  Hamiltonian-Mechanics will only be delivered if a minimum number of 5 (five) students select this course.

Part 3: Introduction to General Relativity (weeks 7-11)
The third part introduces fundamental aspects of General Relativity starting from its Lagrangian formulation.
Contents: Universality of free fall and equivalence principle; Lagrangian formulation of geodesics in General Relativity; curved geometry, geodesics and gravitational red shift; cosmological models.





Degree Programmes for which this Course is Prescribed

  • MA Natural Philosophy
  • MA Philosophy-Physics

Contact Teaching Time

33 hours

This is the total time spent in lectures, tutorials and other class teaching.

Teaching Breakdown


Assessment

1st Attempt: 70% final examination and 30% continuous assessment exercises. Resit: 70 % examination and 30% continuous assessment exercises. Only the marks obtained on the first attempt can count towards Honours classification.

Formative Assessment

By means of class tutorials and dialogue with the lecturer.

Feedback

Feedback on assessments will be given within two weeks or receipt and immediately during classroom exercises.

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