MSP3809 : Variational Methods and Lagrangian Dynamics
MSP3809 : Variational Methods and Lagrangian Dynamics
- Offered for Year: 2025/26
- Module Leader(s): Professor Ian Moss
- Owning School: 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 |
| European Credit Transfer System | |
Pre-requisite
Modules you must have done previously to study this module
| Code | Title |
|---|---|
| MAS2801 | |
| MAS2802 |
Pre Requisite Comment
PHY2026 is acceptable in place of MAS2801
PHY2031 is acceptable in place of MAS2802
Co-Requisite
Modules you need to take at the same time
Co Requisite Comment
N/A
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 | 5 | 1:00 | 5:00 | Problem Classes |
| Scheduled Learning And Teaching Activities | Lecture | 2 | 1:00 | 2:00 | Revision Lectures |
| Scheduled Learning And Teaching Activities | Lecture | 20 | 1:00 | 20:00 | Formal Lectures |
| Guided Independent Study | Assessment preparation and completion | 15 | 1:00 | 15:00 | Completion of in-course assessments |
| Guided Independent Study | Assessment preparation and completion | 58 | 1:00 | 58:00 | Preparation time for lectures, background reading, coursework review |
| Total | 100:00 |
Jointly Taught With
| Code | Title |
|---|---|
| MAS8809 | Variational Methods and Lagrangian Dynamics |
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.
Reading Lists
Assessment Methods
The format of resits will be determined by the Board of Examiners
Exams
| Description | Length | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|---|
| Written Examination | 120 | 2 | A | 85 | N/A |
Exam Pairings
| Module Code | Module Title | Semester | Comment |
|---|---|---|---|
| Variational Methods and Lagrangian Dynamics | 2 | N/A |
Other Assessment
| Description | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|
| Prob solv exercises | 2 | M | 5 | Problem-solving exercises assessment |
| Prob solv exercises | 2 | M | 5 | Problem-solving exercises assessment |
| Prob solv exercises | 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/
- MSP3809's Timetable
Past Exam Papers
- Exam Papers Online : www.ncl.ac.uk/exam.papers/
- MSP3809's past Exam Papers
General Notes
N/A
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The information contained within the Module Catalogue relates to the 2025 academic year.
In accordance with University Terms and Conditions, the University makes all reasonable efforts to deliver the modules as described.
Modules may be amended on an annual basis to take account of changing staff expertise, developments in the discipline, the requirements of external bodies and partners, staffing changes, and student feedback. Module information for the 2026/27 entry will be published here in early-April 2026. Queries about information in the Module Catalogue should in the first instance be addressed to your School Office.