NIU PHYS 600 - Classical Mechanics, Fall 2016

Course contents

1. Introduction to group theory (lecture notes)
   
   
2. Equations of motion from the variational principles
   • Generalized coordinates
   • The principle of least action
   • The Euler-Lagrange equations of motion
   
   
3. The Hamilton and Weiss variational principles and the Hamilton equations of motion
   • Hamilton's principle and the Lagrangian
   • Weiss' action principle and the Hamiltonian
   
   
4. The relation between the Lagrangian and the Hamiltonian descriptions
   
   
5. Symmetries and conservation laws
   • Homogeneity of time and conservation of energy
   • Homogeneity of space and conservation of linear momentum
   • Isotropy of space and conservation of angular momentum
   • A more general treatment of the conservation laws and the action principle
   • Constraints
   
   
6. The central force problem
   • The equivalent one-dimensional problem
   • Classification of orbits
   • The virial theorem
   • Differential equations of the orbit
   • The Kepler problem: the inverse-square law of force
   • Scattering in a central force field
   
   
7. Rigid body motion
   • Coordinate transformation under rotation
   • Orthogonal transformations
   • The equations of motion
   • Angular momentum of a rigid body
   • The symmetrical top
   
   
8. Small oscillations
   • The equations of motion
   • Normal modes
   • Forced vibrations
   • Damped oscillations
   
   
9. Invariance properties of the Lagrangian and Hamiltonian descriptions
   • Poisson and Lagrange brackets
   • Canonical transformations
   • Group properties and methods of constructing canonical transformations
   
   
10. Special relativity
    • From Galilean to Lorentz transformation of space-time
    • Covariant formulation of special relativity - the Minkowski metric tensor, the Poincaré group and its algebra
    • Relativistic adaptation of Hamiltonian and Lagrangian dynamics (lecture notes)
    
    
11. Stability and chaos (time permitting)