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 
EulerLagrange 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,
nonautonomous 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 