Course curriculum

  • 1

    Course Overview

    • Course Overview

    • Study Text
  • 2

    Tutorial 1: Lagrangian Mechanics

    • Study Notes 1

    • 1.1 Introduction

    • 1.2 Action Principle

    • 1.3 Integrals of Motion

    • 1.4 Noether's Theorem

    • 1.5 Noether's Theorem Proof

    • Tutorial 1

    • Tutorial 1 Solutions
  • 3

    Tutorial 2: Introduction to Differential Geometry - Manifolds and Tensors

    • Study Notes 2

    • 2.1 Manifolds

    • 2.2 Objects on a Manifold

    • 2.3 Tangent Vectors

    • 2.4 Cotangent Vectors

    • Tutorial 2

    • Tutorial 2 Solutions
  • 4

    Tutorial 3: Lie Derivative, Differential Forms, Geometric Formulation of Lagrangian Mechanics

    • Study Notes 3

    • 3.1 Tensors

    • 3.2 Differentiation on a Manifold

    • 3.3 Lie Derivative

    • 3.4 Differential Forms

    • 3.5 Geometric Formulations of Lagrangian Mechanics

    • Tutorial 3

    • Tutorial 3 Solutions
  • 5

    Tutorial 4: Hamiltonian Mechanics - Hamilton's Equations, Poisson Brackets, Canonical Transformations

    • Study Notes 4

    • 4.1 Hamilton Canonical Equations

    • 4.2 Legendre Transform

    • 4.3 Poisson Brackets

    • 4.4 Canonical Transformations

    • 4.5 Remarks on Canonical Transformations

    • Tutorial 4

    • Tutorial 4 Solutions
  • 6

    Tutorial 5: Hamilton-Jacobi Equation and Complete Integrability

    • Study Notes 5

    • 5.1 Time Evolution

    • 5.2 Hamilton Jacobi Theory

    • 5.3 Example

    • 5.4 Integrable Systems
  • 7

    Tutorial 6: Constraints, Introduction to Symplectic Geometry

    • Study Notes 6

    • 6.1 Constraints I

    • 6.2 Constraints II

    • 6.3 Symplectic Structure

    • 6.4 Hamiltonian Vector Fields

    • 6.5 Poisson Brackets and Darboux Theorem

    • Tutorial 5

    • Tutorial 5 Solutions
  • 8

    Tutorial 7: Geometric Formulations of Hamiltonian Mechanics

    • Study Notes 7

    • 7.1 Symplectic Geometry Review

    • 7.2 Geometrical Hamiltonian Mechanics

    • 7.3 Canonical Transformations

    • 7.4 Phase Space Noether Theorem

    • 7.5 Hidden Symmetries

    • 7.6 Nambu Mechanics

    • Tutorial 6

    • Tutorial 6 Solutions
  • 9

    Tutorial 8: Contact Geometry, Hamilton-Jacobi Theory Revised, Summary

    • 8.1 Contact Geometry

    • 8.2 Time Dependent Hamiltonian Mechanics

    • 8.3 Hamilton Jacobi Revisited

    • 8.4 Summary and Future Directions