# Math20512

### FAQ

This gives the approximate coverage of topics, lecture by lecture. Text in green is not yet covered.

#### Chapter 1: Newton's Laws

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.

#### Chapter 2: Lagrangian Mechanics

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.

#### Chapter 3: Potential wells and Oscillations

12. (ctd) Potential wells, Equilibria, Hill's region, Stability

13. Harmonic Oscillators: uncoupled and coupled

14. ... coupled harmonic oscillators.

Easter break

15. beats and energy exhange.

16. An anharmonic oscillator (the plane pendulum) and (briefly) Higher dimensional case anharmonic oscillators.

#### Chapter 4: Hamiltonian Mechanics

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.

#### Chapter 5: Rotating Frames (not covered this year)

20. Change of frame

21. Coriolis and centrifugal accelerations/forces.

22. Example (bead in rotating hoop)

JM

Page last modified on Thu, 09 May 2013, at 15:40 (BST)
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