Physical Dynamics

Physical Dynamics (PhD | SPA5304)

Please consult QMPlus for the authoritative information on this module.

Year: 2 | Semester: B | Level: 5 | Credits: 15

Prerequisites: Mathematical Techniques 3 or equivalent for associate students
Lectures: 30 | Lec: 212 311 312 Ex: 509 510 (notation)
Exam: 2.5 hour written paper (75%), coursework (25%)
Practical work: none | Ancillary teaching: Weekly exercises

Course organiser: Dr Masaki Shigemori | Course deputy: Prof Gabriele Travaglini

Synopsis:
Introduction to Lagrangian and Hamiltonian formulations of Newtonian mechanics. Origin of Conservation Laws and their relation to symmetry properties. Rotational motion of rigid bodies, Euler's equations, principal axes and stability of rotation, precession. Small vibration approximation, normal modes.
Aims:
The aim of this course is to generalize the concepts of vector Newtonian mechanics of point particles in order to explore the relation between symmetry, geometry and conservation principles in physics.
Outcomes:
A student who successfully completes this course will be able to: state the vector Newtonian equations of motion for a system of point particles and express them in terms of total linear and angular momentum; state the Newtonian conservation laws for systems of particles, relating them to properties of the forces acting on the particles; define and use the centre of mass frame of reference, expressing linear and angular momentum of a many-particle system in terms of centre of mass variables; describe simple mechanical systems in curvilinear coordinate systems by use of the Lagrangian equations of motion; explain the link between symmetry and conservation laws in the Lagrangian formalism; describe rotating mass distributions in terms of an angular velocity vector and a moment of inertia tensor; derive the Lagrange equations of motion from a variational principle; obtain the Hamiltonian description of a system starting from the Lagrangian picture; describe the geometry of mechanical evolution in phase space.

Recommended books:

Goldstein, H., Poole, C., Safko, J.
Classical Mechanics
Pearson Education (2001)
ISBN-10: 0321188977
ISBN-13: 978-0321188977

Landau, L. D. and Lifschitz, E. M.
Mechanics (third edition)
Course of Theoretical Physics, Volume 1
Butterworth-Heinemann (1982)
ISBN-10: 0750628960
ISBN-13: 978-0750628969

Hand, L. N. and Finch, J. D.
Analytical Mechanics
Cambridge University Press (1998)
ISBN-10: 0521575729
ISBN-13: 978-0521575720

Juno Champion

The school holds Juno Champion status, the highest award of this IoP scheme to recognise and reward departments that can demonstrate they have taken action to address the under-representation of women in university physics and to encourage better practice for both women and men.