Geometry and Mechanics

Rouslan Krechetnikov (University of Alberta)

Jan 1, 2023 — Apr 30, 2023

About the course

This course offers a concise, but self-contained, introduction to the subject of mechanics, which combines geometrical view and physical insights. We will start with a formulation of classical mechanics in the framework of variational principles, translate from point to continuous systems, and analyze the effects of holonomic and nonholonomic constraints. The discussion of effects of friction and collision will naturally lead us to ergodic theory. A significant part of the course will be devoted to the geometric language of mechanics including analysis on manifolds, Lie groups, and differential topology. Among its applications, we will focus on symmetries, reduction, and geometric phase both in finite and infinite dimensions including fluid mechanics. Two key references which define the spirit of the course are “Lectures on Mechanics” by Jerrold Marsden and “Mathematical Methods of Classical Mechanics” by Vladimir Arnold.


This course is available for registration under the Western Dean's Agreement. To register, you must obtain the approval of the course instructor and you must complete the Western Dean's agreement form , using the details below. The completed form should be signed by your home institution department and school of graduate studies, then returned to the host institution of the course.

Enrollment Details

Course Name
Geometry and Mechanics
Jan 1, 2023 — Apr 30, 2023
Course Number
Math 623
Section Number
Section Code


For help with completing the Western Dean’s agreement form, please contact the graduate student program coordinator at your institution. For more information about the agreement, please see the Western Dean's Agreement website

Other Course Details