# Unit information: Analytical Mechanics in 2021/22

Unit name Analytical Mechanics PHYS30008 10 H/6 Teaching Block 2 (weeks 13 - 24) Dr. Machon 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 including Unit Aims

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 Information

The unit will be taught through a combination of

• asynchronous online materials, including narrated presentations and worked examples
• synchronous group problems classes, workshops, tutorials and/or office hours
• asynchronous directed individual formative exercises and other exercises
• guided, structured reading

## Assessment Information

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

Summative 2 hour written exam 100%

## Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. PHYS30008).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.

See the Faculty workload statement relating to this unit for more information.

Assessment
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit. The Board considers each student's outcomes across all the units which contribute to each year's programme of study. If you have self-certificated your absence from an assessment, you will normally be required to complete it the next time it runs (this is usually in the next assessment period).
The Board of Examiners will take into account any extenuating circumstances and operates within the Regulations and Code of Practice for Taught Programmes.