This gives the approximate coverage of topics, lecture by lecture. Text in green is not yet covered.
1. Particles: kinetic energy, momentum, angular momentum, Newton's laws (and Galileo's).
2. Circular motion, moment of inertia. Systems of particles.
3. Systems ctd: kinetic energy, centre of mass, conservation of momentum and angular momentum.
4. Continua as limit of systems. Moment of inertia of a rotating body.
5. Conservative forces, potential energy. Conservation of energy.
6. Work for systems of particles. Lorentz force.
7. Moving frames and Galilean transformations. Centre of mass frame.
8. From Newton to Lagrange: equivalence of two equations.
9. Generalized coordinates and degrees of freedom; Lagrangian. Examples
10. Constraints and invariance of Lagrange's equations. Examples.
11. Mass-inertia matrix, regular Lagrangians.
12. Noether's theorem.
12. (ctd) Potential wells, Equilibria, Hill's region, Stability
13. Harmonic Oscillators: uncoupled and coupled
14. ... coupled harmonic oscillators.
15. beats and energy exhange.
16. An anharmonic oscillator (the plane pendulum) and (briefly) Higher dimensional case anharmonic oscillators.
17. generalized momentum, Hamiltonian, Hamiltonian for simple mechanical systems.
18. Hamilton's equations. Equivalence with Lagrange's equations, Noether's theorem revisited, conservation of energy, examples
19. Hamiltonian dynamics: equilibria and stability; the wave equation from the Hamiltonian point of view.
20. Change of frame
21. Coriolis and centrifugal accelerations/forces.
22. Example (bead in rotating hoop)