Analytical Mechanics
Covers the fundamental theories of classical mechanics, and provides a firm grounding for later studies of fluid dynamics and quantum physics.
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. Many worked examples are included to aid the students’ intuition and help them gain confidence and proficiency in problem solving.
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.
A solid background in college-level introductory physics is assumed, therefore a systematic review of elementary mechanics will not be part of this course. Familiarity with certain few basic mathematical concepts is essential. The student should understand Taylor series in more than one variable, partial derivatives, the chain rule, and elementary manipulations with complex variables – say at the level of Advanced Calculus, 2nd Ed, W. Kaplan, Addison-Wesley, 1984 or Calculus and Analytical Geometry, 9th Ed., Thomas & Finney, Addison-Wesley, 1995. Some elementary knowledge of matrices and determinants is also needed – say at the level of Linear Algebra with Applications, 2nd Ed, S. J. Leon, MacMillan 1985 or one of many other equivalent texts at the intermediate level. The student shall have either completed or is concurrently registered in a Mathematical physics course, involving vector analysis, complex variable theory, and techniques for solving ordinary and partial differential equations. However, a thorough grounding in these subjects is not essential and can be picked up during the course.
Mechanics, 4 edn, by Landau and Lifshitz (1976) Butterworth-Heinemann
Classical Mechanics, 3 edn, by Goldstein, Poole, and Safko (2001) Addison Wesley
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