OVERVIEW
LECTURE NOTES
COURSE WORK
Physics 3C03: Analytical Dynamics
Lecture Notes
The lecture notes on this page are mainly selected highlights from the course textbook(s).
1) Conservation of angular momentum and central forces
2) Keplerian orbits
3) Scattering cross-section and Rutherford scattering
4) The two-body problem
5) Rotating frames
6) Foucault pendulum slides
7) Lagrangian Mechanics
8) Ignorable coordinates and constants of motion
9) Small oscillations and normal modes
10) Oscillations of particles on a string and the relation to field theory
11) Rigid body dynamics I: the inertia tensor and the principal axes of inertia
12) Notes on the angular momemtum-torque equations in the centre of mass frame (D.W.L. Sprung)
13) Rigid body dynamics II: the ellipsoid of inertia and the Poinsot construction (D.W.L. Sprung)
14) Rigid body dynamics III: more on the Poinsot construction plus the Binet ellipsoid (D.W.L. Sprung)
15) Rigid body dynamics IV: Euler angles and the spinning top (D.W.L. Sprung)
16) Rigid body dynamics V: motion of a symmetric rigid body in an inertial frame (D.W.L. Sprung)
17) Rigid body dynamics VI: precession and nutation of a symmetric top (D.W.L. Sprung)
18) Rigid body dynamics VII: horizontal precession of a gyroscope (D.W.L. Sprung)
19) Rigid body dynamics VIII: Lagrangian approach to the motion of a symmetric top
20) Charged particle in an EM field plus Poisson brackets
21) Canonical transformations
22) The Hamilton-Jacobi equation and action-angle variables
24) On the connection between Hamilton-Jacobi theory and quantum mechanics: the JWKB approximation
25) Separable Hamiltonians
26) Integrable Hamiltonians: motion on tori in phase space
27) A brief summary of the KAM theorem
28) An introduction to chaos
29) Slides for Poincaré sections and maps (including the Mandelbrot set and the logistic map)
30) Fixed points of maps
31) The Poincaré-Birkhoff theorem and the break-up of tori in chaotic maps
[
Overview
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Lecture Notes
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Course Work
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