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Module

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

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.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Guided Independent StudyAssessment preparation and completion581:0058:00Preparation time for lectures, background reading, coursework review
Scheduled Learning And Teaching ActivitiesLecture51:005:00Problem Classes
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision Lectures
Scheduled Learning And Teaching ActivitiesLecture201:0020:00Formal Lectures
Guided Independent StudyAssessment preparation and completion151:0015:00Completion of in-course assessments
Total100:00
Jointly Taught With
Code Title
MAS8809Variational 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.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Exams
Description Length Semester When Set Percentage Comment
Written Examination1202A85N/A
Exam Pairings
Module Code Module Title Semester Comment
Variational Methods and Lagrangian Dynamics2N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M5Problem-solving exercises assessment
Prob solv exercises2M5Problem-solving exercises assessment
Prob solv exercises2M5Problem-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.

Reading Lists

Timetable