Chapter 1

Lagrangian Formulation

Degrees of freedom

medium • 1 min read

Generalized coordinates

medium • 2 min read

D'Alembert's principle

medium • 3 min read

Euler-Lagrange equations

medium • 4 min read

Applications of Lagrangian method

medium • 5 min read

Chapter 2

Hamiltonian Formulation

Generalized momenta

medium • 1 min read

Hamilton's principle

medium • 2 min read

Hamilton's canonical equations

medium • 3 min read

Derivation of Hamilton's equations

medium • 4 min read

Phase space behavior

medium • 5 min read

Chapter 3

Central Force Motion and Scattering

Reduction to one-body problem

medium • 1 min read

Equation of motion for central force

medium • 2 min read

Effective potential

medium • 3 min read

Artificial satellites dynamics

medium • 4 min read

Rutherford scattering cross-section

medium • 5 min read

Chapter 4

Special Theory of Relativity

Michelson-Morley experiment

medium • 1 min read

Lorentz transformations

medium • 2 min read

Length contraction and time dilation

medium • 3 min read

Addition of velocities

medium • 4 min read

Relativistic momentum and energy

medium • 5 min read