MSP3809
Variational Methods and Lagrangian Dynamics
- Offered for Year: 2025/26
- Module Leader(s): Professor Ian Moss
- Owning School: School of Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
Semesters
Your programme is made up of credits, the total differs on programme to programme.
| Semester 2 Credit Value: | 10 |
| ECTS Credits: | 5.0 |
Aims
To present basic ideas and techniques of variational calculus and Lagrangian dynamics.
Review of standard methods for finding extrema. Definition of, and method for calculating, extremals (minima/maxima) of functionals. The Euler-Lagrange equation. Classical examples from different disciplines.
Lagrange multipliers. Multiple fields and variables.
The action principle and the Lagrangian, Generalized momenta. Euler angles. Hamiltonian dynamics, with applications to astro- and particle physics.
Outline Of Syllabus
Students will gain an understanding of basic variational problems and their importance in various applications.
Learning Outcomes
Intended Knowledge Outcomes
Students will gain an understanding of basic variational problems and their importance in various applications.
Intended Skill Outcomes
Students will be able to solve a range of basic variational problems with and without constraints. Students will be able to identify and solve a range of minimisation problems such as ‘what is the shortest distance between two points on a plane’ or ‘how to curve a string of given length to enclose the largest area’. They will be able to formulate advanced problems in astro and particle physics using Hamilton’s principle.
Students will develop skills across the cognitive domain (Bloom’s taxonomy, 2001 revised edition): remember, understand, apply, analyse, evaluate and create.
Teaching Methods
Teaching Activities
| Category | Activity | Number | Length | Student Hours | Comment |
|---|---|---|---|---|---|
| Scheduled Learning And Teaching Activities | Lecture | 20 | 1:00 | 20:00 | Formal Lectures |
| Scheduled Learning And Teaching Activities | Lecture | 2 | 1:00 | 2:00 | Revision Lectures |
| Scheduled Learning And Teaching Activities | Lecture | 5 | 1:00 | 5:00 | Problem Classes |
| Guided Independent Study | Assessment preparation and completion | 58 | 1:00 | 58:00 | Preparation time for lectures, background reading, coursework review |
| Guided Independent Study | Assessment preparation and completion | 15 | 1:00 | 15:00 | Completion of in-course assessments |
| Totals | 100 |
Teaching Rationale And Relationship
Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.
The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking.
Assessment Methods
The format of resits will be determined by the Board of Examiners.
Exams
| Component | Length (mins) | Semester | When set | Percentage | Comment |
|---|---|---|---|---|---|
| Written Examination 1 | 120 | 2 | A | 85 | N/A |
Other Assessments
| Component | Semester | When set | Percentage | Comment |
|---|---|---|---|---|
| Problem solving exercises 1 | 2 | M | 5 | Problem-solving exercises assessment |
| Problem solving exercises 2 | 2 | M | 5 | Problem-solving exercises assessment |
| Problem solving exercises 3 | 2 | M | 5 | Problem-solving exercises assessment |
Assessment Rationale And Relationship
A substantial formal unseen examination is appropriate for the assessment of the material in this module. the format of the examination will enable students to reliable demonstrate their own knowledge, understanding and application of learning outcomes. the assurance of academic integrity forms a necessary part of the programme accreditation.
Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one way for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating theor ideas and explicitly citing the theory they are using.
The coursework assignments allow the students to develop their problem-solving techniques, to practice the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.
Timetable
- Timetable Website: www.ncl.ac.uk/timetable/