About the Course
This course provides a comprehensive introduction to Theoretical Mechanics, developing the fundamental frameworks used to describe classical systems beyond the Newtonian approach. Beginning with Lagrangian mechanics, we learn how to formulate equations of motion using energy principles and the principle of least action, with an emphasis on generalized coordinates and the systematic treatment of constraints. The course then introduces Hamiltonian mechanics, recasting dynamics in terms of phase space and canonical variables, and highlighting the role of symmetries and conservation laws. Techniques for handling constraint forces, including holonomic constraints and Lagrange multipliers, are integrated throughout. Applications include the dynamics of rigid bodies, with a detailed study of rotational motion using Euler angles and moments of inertia, as well as the two-body problem, where central force motion is reduced and analyzed to understand orbital dynamics. We will also talk about chaotic motion and phase spaces. The course emphasizes both mathematical formulation and physical interpretation, providing a foundation for advanced study in classical mechanics, quantum mechanics, and related fields.
Textbooks
There are lots of good textbook are the website. Some of my favorite are:
- Classical Mechanics by John Taylor: This is the standard undergraduate book, providing clear explanations with lots of worked problems. The book covers Lagrangian mechanics, Hamiltonian mechanics, central forces, analysis of chaotic motion, and e.t.c.
- Introduction to Classical Mechanics by Morin: Compare to Classical Mechanics by Taylor, Morin provides more challenging problems. The book is good for sharpening problem-solving skills.
- Modern Classical Mechanics by Helliwell & Sahakian: The textbook is math heavy but shows the full derivation of the Euler-Lagrange equation, Euler angles, and e.t.c. It also provides tons of worked examples, which are very helpful. This is the textbook the notes mainly relies on.
Topics
| Topics | Details |
| Newtonian Mechanics | |
| Relativity | |
| The Variation Principle | • Fermet’s Principle • The Calculus of Variation • Geodesics • Brachistochrone • Several Dependent Variables • Mechanics From a Variation Principle • Motion in a Uniform Field |
| Lagrangian Mechanics | • Non-conservative forces • Forces of Constraints and Generalized • Coordinates • Introduction to Hamilton’s Mechanics • Systems of Particles • Generalized Momenta and Cyclic Coordinates • Hamiltonian • Hamiltonian and Energy |
| From Classical to Quantum | |
| Constraint and Symmetry | |
| Gravitation | |
| Electromagnetism | Scattering Additional Note |
| Accelerating Frames | |
| Hamiltonian Formulation | |
| Rigid Body Dynamics | |
| Coupled Oscillators |