Analytical Mechanics

Course Aim

Covers the fundamental theories of classical mechanics, and provides a firm grounding for later studies of fluid dynamics and quantum physics.

Course Description

Explore the concepts and techniques of classical analytical mechanics so essential to a deep understanding of physics, particularly in the areas of fluid dynamics and quantum mechanics. Develop from the basic principles of symmetry and least action to the Galilean, Lagrangian, and Newtonian equations of motion and laws of conservation.  Use the Lagrange formalism to describe particle motion in multiple modes, before exploring the equations of Euler and Hamilton, and canonical transformations.  Use the calculus of variation to develop Maupertuis's principle and the Hamilton-Jacobi equations, and build a starting point for the consideration of waves in other courses.  Ongoing homework exercises and small exams provide continuing assessment.

Course Contents

Lagrangian Mechanics
Variational Calculus
Linear Oscillators
Central Forces
Noether’s theorem & Hamiltonian Dynamics
Canonical Transformations & Action-Angle Variables
Canonical Transformations & Action-Angle Variables
Rotating Coordinate Systems
Dynamics of Rigid Bodies
Theory of Small Vibrations
Review + Optional advanced topics


Weekly assignments: 30% of total grade Mid-term exam: 30% of total grade Final exam: 40% of total grade.

Prerequisites or Prior Knowledge

College level introductory physics or permission of instructor, mathematics for physics.


Mechanics, 4 edn, by Landau and Lifshitz (1976) Butterworth-Heinemann
Classical Mechanics, 3 edn, by Goldstein, Poole, and Safko (2001) Addison Wesley

Reference Books

The Variational Principles of Mechanics, 4 edn, Cornelius Lancoz (1970) Dover
The Feynman Lectures on Physics including Feynman's Tips on Physics: The Definitive and Extended Edition, 2 edn, by RP Feynman with Robert B. Leighton et al., editors (2005) Addison Wesley

Research Specialties