Classical Mechanics
Notes on constraints, analytical mechanics, and central-force motion.
Classical mechanics
Constraints restrict the motion a system can make. Generalized coordinates incorporate that geometry, and virtual work separates the equations of motion from ideal reactions. The Lagrangian and Hamiltonian formulations then organize the same mechanics through energies and momenta. Central-force motion brings these ideas together in the dynamics of orbits.
The four units follow the supplied syllabus. Mathematical prerequisites introduce the background needed to begin; later chapters develop additional polar and vector relations where they are used. The full derivations of Lagrange's and Hamilton's equations are collected in an optional appendix, as the syllabus specifies.
Unit 1 · Constrained motion
Unit review · Hints and solutions
Unit 2 · Lagrangian formalism
| Chapter | Topic |
|---|---|
| 7 | The Lagrangian and equations of motion |
| 8 | Applied forces and dissipation |
| 9 | Momentum, symmetry, and conservation |
| 10 | The kinetic-energy function |
| 11 | Moving constraints and coupled motion |
Unit review · Hints and solutions
Unit 3 · Hamiltonian formalism
| Chapter | Topic |
|---|---|
| 12 | From the Lagrangian to the Hamiltonian |
| 13 | Phase space and Hamilton’s equations |
| 14 | Energy and forces in Hamiltonian mechanics |
| 15 | Hamiltonian applications and comparisons |
Unit review · Hints and solutions
Unit 4 · Central-force motion
Unit review · Hints and solutions
Course references
Formula sheet · Derivation index · Definition index · Concept connections · Problem bank · Final revision
Exercises are collected at the end of each chapter, with solutions on separate pages. The syllabus coverage table records the location and scope of every prescribed topic.