Topics in Advanced Dynamics

Central Forces-Bertrand’s Theorem
Central Forces-Impulsive Orbit Perturbations 
Scattering-Inverse Scattering
Scattering-Truncated Coulomb Potential (Rydberg Scattering)
Scattering-Inverse Cube Scattering 
Noninertial Reference Frames-Gravity String
Rigid Body Motion-Spinning Top
Rigid Body Motion/Noninertial Reference Frames-Gyrocompass
Small Oscillations /Noninertial Reference Frames-Lagrangian Points
Oscillations and Waves-Spherical Pendulum
Oscillations and Waves-Finite Chain 

Topics in Variational Mechanics 

Mechanics Roadmap
Constraints and Generalized Coordinates
Two Potential Formalism
Review of Lagrangian Formalism
Direct Derivation of D’Alembert’s Equations
Hamiltonian Formalism
Legendre Transforms
Conditions of the Construction of Lagrangians, Hamiltonians
Schwinger Variational Viewpoint
Maupertis Principle of Action (Endpoint Variation of Independent Degrees of Freedom in the Action) 
Noether’s Theorem (Endpoint Variation of Dependent Degrees of Freedon in the Action) 
Canonical Transformations
Poission Bracket Formalism
Infinitismal Canonical Tranformations and Generators
Symplectic Formalism
Dissipative Systems and Louiville’s Theorem
Hamilton-Jacobi Equation and Formalism
Action-Angle Variables (Formalism and Quick and Dirty Derivation)
Classical/Quantum Correspondences

Topics in Nonlinear Dynamics

Secular Perturbation Theory
Types of Stability
Stability for Hamiltonian Systems
Orbital Stability
Poincaire Sections
Characteristic Multipliers
Bifurcations and Period Doubling
The Logistic Map
Indications of Deterministic Chaos
Routes to Deterministic Chaos
Lyapunov Exponents
Fractals