Last modified: 25 May 2018 11:16
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.
| Study Type | Undergraduate | Level | 4 |
|---|---|---|---|
| Term | Second Term | Credit Points | 15 credits (7.5 ECTS credits) |
| Campus | None. | Sustained Study | No |
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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.
Information on contact teaching time is available from the course guide.
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.
By means of class tutorials and dialogue with the lecturer.
Feedback on assessments will be given within two weeks or receipt and immediately during classroom exercises.
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