| We ek |
Date | Contents | References |
Lec |
| 1 | 0904 |
UBC Imagine Day | ||
| 0906 | outline Part I. Newtonian Mechanics The principles of relativity and determinacy, the galilean group and Newton's equations |
1.1, 1.2 |
1 | |
| 2 | 0911 | (merged to other lectures) |
||
| 0913 | ||||
| 3 | 0918 | examples, potential energy, investigation of systems
with one degree of freedom |
1.3, 2.4 |
2 |
| 0920 | systems
with two degrees of freedom, central fields and conservation of angular
momentum, Kepler's second law |
2.5 - 2.7 |
3 | |
| 4 | 0925 | motion in 2D central fields, effective potential 3D motion of n particles, conservation of momentum, center of mass |
2.8 - 2.10 |
4 |
| 0927 |
conservation of angluar momentum and energy for n particles, two body problem Part II. Constraint Free Lagrangian Mechanics calculus of variations |
2.10, 3.12 |
5 | |
| 5 | 1002 |
Euler-Lagrange equations, Lagrange's equations of mechanics,
Legendre transform |
3.12 - 3.14 |
6 |
| 1004 |
duality of Legendre transform and Young's inequality, Hamilton's
equations, phase flow and Liouville's theorem
|
3.14 - 3.16 |
7 | |
| 6 | 1009 |
Poincare recurrence theorem Part III. Lagrangian Mechanics on manifolds holonomic constraints, topological and differentiable manifolds |
3.16, 4.17, 4.18 |
8 |
| 1011 |
examples, embedding and immersion, tangent space and tangent bundle |
4.18 |
9 | |
| 7 | 1016 |
tangent bundle, derivative map, Riemannian manifolds, motion in
a lagrangian system |
4.18, 4.19 |
10 |
| 1018 |
free motion on a surface of revolution, geodesics,
non-autonomous lagrangian system |
4.19 |
11 | |
| 8 | 1023 |
motion on rotating vertical circle, Noether's theorem |
4.19, 4.20 |
12 |
| 1025 |
Noether's theorem, minimization with integral constraints
|
4.20, * |
13 | |
| 9 | 1030 |
minimization with pointwise constraints, linearization |
*, 5.22 |
14 |
| 1101 |
small oscillations |
5.23 |
15 | |
| 10 | 1106 |
example 3 behavior of char. frequencies under change of rigidity or imposition of constraint, minimax characterization of eigenvalues |
5,23, 5.24 |
16 |
| 1108 |
proof of theorems in §5.24, periodic systems |
5.24, 5.25 |
17 | |
| 11 | 1113 |
parametric resonance |
5.25 |
18 |
| 1115 |
inverted pendulum with oscillating point of suspension motion in a moving coordinate system, inertial forces and Coriolis force |
5.25 6.26, 6.27 |
19 | |
| 12 |
1120 |
falling rock, cyclone orientation, Foucault
pendulum |
6.27 |
20 |
| 1122 |
motion of a rigid body is limited to a 2D torus, inertia
operator |
6.28 |
21 | |
| 13 |
1127 |
inertia ellipsoid, Euler's equations for dynamics of a rigid body with a fixed point |
6.28, 6.29 |
22 |
| 1129 |
Poinsot's description of the motion |
6.29 |
23 | |
| Final exam |