Classical Mechanics
Classical Mechanics
Contents
- Newtonian Mechanics Review
- Generalised Coordinates and Constraints
- Lagrangian Mechanics
- Hamiltonian Mechanics
- Noether”s Theorem and Conservation Laws
- Central Force Problems
- Small Oscillations and Normal Modes
- Rigid Body Dynamics
- Problem Set
- Rigid Body Dynamics: Advanced Topics
- Hamiltonian Mechanics: Advanced Topics
- Nonlinear Dynamics and Chaos
- Classical Field Theory
Overview
University-level classical mechanics notes covering Lagrangian, Hamiltonian, and advanced topics.
Topics Covered
- Lagrangian Mechanics: Generalised coordinates, Euler-Lagrange equations, constraints
- Hamiltonian Mechanics: Phase space, canonical transformations, Hamilton-Jacobi theory
- Central Force Problems: Kepler orbits, scattering, potential theory
- Rigid Body Dynamics: Rotations, inertia tensor, Euler equations
Prerequisites
- Newtonian mechanics (forces, energy, momentum)
- Multivariable calculus (partial derivatives, integrals)
- Linear algebra (vectors, matrices)
- Basic differential equations
How to Use These Notes
Start with Lagrangian mechanics to build foundational knowledge, then progress to Hamiltonian mechanics and advanced topics. Each section includes worked examples and practice problems.
Navigation
Use the sidebar to browse topics, or start with the introductory pages linked from the sidebar.
Additional Resources
Each section includes:
- Detailed explanations of key concepts
- Worked examples with step-by-step solutions
- Practice problems with answers
- Common pitfalls and how to avoid them
- Connections to other areas of physics
Study Tips
- Master Lagrangian mechanics: Understand the principle of least action and generalised coordinates
- Practise problems: Work through many problems to build intuition
- Draw diagrams: Visualise coordinate systems and phase space
- Learn symmetries: Understand Noether’s theorem and conservation laws
- Connect to advanced physics: Relate classical mechanics to quantum mechanics and field theory