Lagrangian and Hamiltonian Dynamics
SCQF Level 10
Academic year(s): 2019-2020
SCOTCAT credits : 15
ECTS credits : 7
Level : SCQF Level 10
Availability restrictions: Not automatically available to General Degree students
The module covers the foundations of classical mechanics as well as a number of applications in various areas. Starting from the principle of least action, the Lagrangian and Hamiltonian formulations of mechanics are introduced. The module explains the connection between symmetries and conservation laws and shows bridges between classical and quantum mechanics. Applications include the central force problem (orbits and scattering) and coupled oscillators.
Pre-requisite(s): Before taking this module you must pass PH3081 or pass PH3082 or ( pass MT2506 and pass MT2507 ). In taking this module you will need a knowledge of vector calculus
Anti-requisite(s): You cannot take this module if you take MT4507
Weekly contact: 2 or 3 lectures and some tutorials
Scheduled learning hours: 32
Guided independent study hours: 118
As used by St Andrews: 2-hour Written Examination = 75%, Coursework = 25%
As defined by QAA
Written examinations : 75%
Practical examinations : 0%
Re-assessment: Oral Re-assessment, capped at grade 7
Module coordinator: Dr B H Braunecker
Module teaching staff: Dr B Braunecker
To give students a solid grounding and sufficient training in Lagrangian and Hamiltonian techniques in classical mechanics and their applications, including
By the end of the module, students will have a solid knowledge of the central concepts of Classical Mechanics and will have acquired and trained important problem-solving skills. They will be able to
Review of Newtonian mechanics.
Equations of Motion: The Principle of least action. The Euler-Lagrange equations. Free and interacting particles in non-relativistic mechanics. Introductory examples to illustrate the abstract concepts that follow in sections 2 and 3.
Conservation Laws: Energy, momentum, angular momentum, centre of mass. The Noether theorem.
Canonical formalism: Hamiltonian techniques. Canonical transformations. Liouville theorem (Hamilton-Jacobi theory).
Applications: Two-body problem. Kepler problem (planetary motion). Collisions.
Additional information on continuous assessment etc.
Please note that the definitive comments on continuous assessment will be communicated within the module. This section is intended to give an indication of the likely breakdown and timing of the continuous assessment.
This module is typically taken in JH by theoretical physicists, and in SH by those doing an MPhys in other degree programmes in the School. It is sufficiently core to the programmes that it is included in the summary of deadlines etc on the School’s Students and Staff web pages. Five tutorial sheets will be issued over the semester in two week intervals. They contain questions that will deepen the understanding of the current topics in the lectures, and they are required to be handed in for marking. This accounts for 25% of the module mark. Tutorials take the form of “whole class” tutorials where the solutions and underlying physics and problem-solving strategies can be discussed.
This module may not contain material that is part of the IOP “Core of Physics”, but does contribute to the wider and deeper learning expected in an accredited degree programme. The skills developed in this module, and others, contribute towards the requirements of the IOP “Graduate Skill Base”.
Please view University online record:
Please also read the general information in the School's honours handbook that is available via st-andrews.ac.uk/physics/staff_students/timetables.php