# Unit information: Analytical Mechanics in 2019/20

Please note: Due to alternative arrangements for teaching and assessment in place from 18 March 2020 to mitigate against the restrictions in place due to COVID-19, information shown for 2019/20 may not always be accurate.

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Unit name Analytical Mechanics PHYS30008 10 H/6 Teaching Block 2 (weeks 13 - 24) Professor. Annett Not open Level I/5 Mathematical Physics PHYS23020 This course MAY NOT be taken with MATH21900 Mechanics2, MATH31910 Mechanics 23 School of Physics Faculty of Science

## Description

This course introduces the fundamental mathematical methods used in theoretical classical mechanics. These in turn provide the necessary foundations for quantum mechanics, statistical physics and quantum field theory, which are the core theoretical tools used in all of modern physics. Aims: to build upon the students' prior knowledge of Newtonian mechanics and special relativity and show that these can be understood within a deeper and more powerful mathematical framework. Students will learn to solve complex mechanical problems using the more powerful methods provided by the Lagrangian and Hamiltonian formulations of mechanics.

## Intended learning outcomes

Students will be able to:

Perform calculations and demonstrate understanding of basic techniques of Lagrangian mechanics, such as constrained mechanical systems, simple relativistic systems, or charged particles in a magnetic field.

Evaluate and interpret Coriolis and centrifugal forces within the context of Lagrangian and Hamiltonian mechanics, for example to solve problems in planetary motion, or for spinning tops.

Evaluate and interpret Coriolis and centrifugal forces within the context of Lagrangian and Hamiltonian mechanics, for example to solve problems in planetary motion, or for spinning tops.

Interpret the analogy between mechanical and optical systems

Derive the canonical momentum and Hamiltonian for systems defined by a Lagrangian, and to solve the corresponding Hamilton's equations of motion

Solve problems relating to phase space motion of a dynamical system, applying Liouville's theorem as appropriate

Apply general variational principles, such as the principle of least action in mechanical problems

## Teaching details

Lectures, problems classes, independent study

## Assessment Details

Formative - problem sheets for self-study throughout course; 2 x 2-hour problems classes

Summative 2 hour written exam 100%