Module description
Syllabus:
This course aims to give an introduction to the basic concepts and tools used to study all dynamical systems, from pendulums to falling cats, to the planets, stars and galaxies. The course will cover Newtonian mechanics in three dimensions, vector calculus, inertial frames, linear and angular momentum, multi-particle systems, work, energy, conserved quantities, conservative forces, potentials, central forces, configuration space, Lagrangian systems, the principle of least action, Euler-Lagrange equations, generalised coordinates, constrained systems, Kepler’s laws, Hamiltonian dynamics, Poisson brackets, symmetries, Noether’s theorem, Liouville’s theorem and the Poincare recurrence theorem.
Newtonian, Lagrangian, Hamiltonian mechanics.
Prerequisites:
Normally 4CCM131a Introduction to Dynamical Systems.
Assessment details
2 hour written examination.
Semester 1 only students will be set an alternative assessment in lieu of in-person exams in January.
Full year students will complete the standard assessment.
Educational aims & objectives
The aim of the module is to develop the central concepts and mathematical techniques of classical Newtonian mechanics in three dimensions, focusing on Lagrangian and Hamiltonian methods. The module aims to lay the foundation for further studies in topics such as quantum theory, statistical mechanics, and chaos.
Learning outcomes
To be able to construct Lagrangians for a range of physical systems, obtain the Euler-Lagrange equations, identify conserved quantities and use these to simplify the equations of motion. Construct Hamiltonians and understand various general theorems about phase space and Hamiltonian flows.
Teaching pattern
Three hours of lectures and one hour of tutorial per week throughout the term
Suggested reading list
Indicative reading list - link to Leganto system where you can search with module code for lists