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Module

MAS3809 : Variational Methods and Lagrangian Dynamics

  • Offered for Year: 2020/21
  • Module Leader(s): Professor Ian Moss
  • Owning School: Mathematics, Statistics and Physics
  • Teaching Location: Newcastle City Campus
Semesters
Semester 2 Credit Value: 10
ECTS Credits: 5.0

Aims

To present basic ideas and techniques of variational calculus, including relevant applications.

Module Summary
What is the shortest route between two places on the Earth's surface (the answer isn't a straight line, because the Earth isn't flat!)? What is the optimum roller coaster design that provides the minimum descent time? How do you reformulate dynamical motion in terms of geometry? To answer questions such as these, we need a way to find the path between two points which minimises some quantity (such as length or time). The calculus of variations is a very elegant and powerful way of doing this, and consequently has wide application to real-world problems. The ideas also provide the basis for a reformulation of dynamics which underpins modern theoretical physics.

Outline Of Syllabus

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 everyday life. Fixed
and variable end conditions. Lagrange multipliers. Many dependent variables. The action principle, Lagrangian
and Hamiltonian dynamics with applications.

Teaching Methods

Module leaders are revising this content in light of the Covid 19 restrictions.
Revised and approved detail information will be available by 17 August.

Assessment Methods

Module leaders are revising this content in light of the Covid 19 restrictions.
Revised and approved detail information will be available by 17 August.

Reading Lists

Timetable