Math 428/609E: Mathematical Classical Mechanics

This course is a PIMS Network Course and is also open to the public

Spring Term 2025
Lior Silberman

General Information

This course presents classical mechanics to a mixed audience of mathematics and physics undergraduate and graduate students. It is complementary to regular phsyics courses in that while the physics concepts will be developed the emphasis will be on the underlying mathematical analysis. Students should already have some experience with rigorous mathematics (at UBC via courses like MATH 223, 320, 321), and with classical mechanics (at UBC via courses like PHYS 216). Pre-requisites can be waived: contact the instructor if you wish to discuss this.

References

  1. Arnol'd, Mathematical Methods of Classical Mechanics, available from SpringerLink
  2. Cushman & Bates, Global Aspects of Classical Integrable Systems, available from SpringerLink
  3. Giaquinta & Hildebrandt, Calculus of Variations, available from SpringerLink
  4. Goldstein, Classical Mechanics
  5. Landau & Lifshitz, Course of Theoretical Physics vol. 1: Mechanics
  6. Spivak, Physics for mathematicians—mechanics I

Problem Sets

  1. Problem Set 1 (LyX, TeX), due 16/1/2025. Note: problem F(c) fixed in PDF version.
  2. Problem Set 2 due 30/1/2025. Version updated.
  3. Problem Set 3 due 30/1/2025. Version updated.
  4. Problem Set 4

Lecture-by-Lecture information

Warning: the following information is tentative and subject to change at any time

Chapter Week Date Material In-class Notes
Kinematics 1 T 7/1 Introduction
Configuration space
Scan  
Þ 9/1 Coordinates
Tangent vectors
Scan  
Newtonian
Mechanics
2 T 14/1 Dynamics
Differential Equations
Scan  
Þ 16/1 The Galilean Group
Conservation Laws
Scan PS1 due
3 T 21/1 Examples Scan  
Lagrangian
Mechanics
Þ 23/1 Calculus of Variations Scan  
4 T 28/1 "Direct" appraoch
Sobolev spaces
Scan  
Þ 30/1 Examples Scan  
5 T 4/2 Constraints Scan  
Þ 6/2 Symmetry Scan  
6 T 11/2 Angular momentum Scan  
Þ 13/2 Small Oscillations Scan  
Feb 17-21 UBC Winter break
7 T 25/2 Rigid Body Motion Scan  
Hamiltonian
Mechanics
Þ 27/2 Convex Geometry
The Legendre transformation
Scan  
8 T 4/3 Symplectic Geometry
The Hamiltonian Flow
Scan  
Þ 6/3 Dynamics Scan  
9 T 18/3 Thermodynamics ensembles Scan  
Þ 20/3 Integrable Systems
Hamilton--Jacobi
Scan  
Quantum
Mechanics
10 T 25/3   Scan  
Þ 27/3      
11 T 1/4      
Þ 3/4      
13 T 8/4      
Þ 10/4      
Final exam F 25/4 8:30-11:30 @ BUCH B318    


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Last modified Sunday March 30, 2025