1. Test 2 review Test: 7 pm in 203 MPHY
Material: HW 6-9, Taylor Ch. 6,7,8,14; my notes
Your notes allowed, printed material is not
No calculators, no numbers
Math formulas from Taylor will be given
If you feel you need some formula, don’t hesitate to ask!

2. How to prepare
Review your lecture notes and make sure they are complete
Solve all your homework and posted exams
Solve examples from the book chapters
Solve end of chapter problems
HW solutions are posted, but don’t look at them before you solve the problem!
Don’t hesitate to contact me if you have any difficulties

3. Lagrangian mechanics
Line element and kinetic energy in cylindrical and spherical coordinates
Euler-Lagrange equations and their general properties:
cyclic coordinates and integrals of motion
dropping total derivatives
Similarity and virial theorem
Equilibrium points, linearization, small oscillations!
Lagrangian for a particle in the EM field

4. Problem solving tips
If you are not sure, choose Cartesian coordinates and then convert into any other coordinates
Determine the number of degrees of freedom. Use constraints to eliminate extra variables
Identify and drop total derivatives
Identify cyclic coordinates and use corresponding integrals of motion instead of E-L equations

5. Central force Review chapter 8, class notes, and homework
Conservation of E and L
Properties of orbits in a fixed central force potential
Effective radial motion and potential
Circular orbits
Applying virial theorem
Orbits in a gravitational field. General formula
p/r = 1 + ecosφ. Definition of r_min, r_max, energy and angular momentum of the orbit
Changing parameters, changing orbits, tangential boosts

6. Two-body problem
Relationship between C.O.M. and lab frames for radius-vectors, velocities, momenta. Relative motion, μ-point
Lagrangian for the relative and COM motion. E-L equations
Presence of external forces

7. Collisions and scattering
C.o.m. and lab frames: conservation laws. Relationship between c.o.m. and lab frames
Kinematic formulas for angles, velocities, momenta etc.
Formulation of the scattering problem
Impact parameter, scattering angle, solid angle
Scattering cross-section in the c.o.m. and lab frames (for incident particles and targets)

8. Special cases Coulomb scattering
Scattering by an elastic surface of revolution
Capture by an attractive center and by a finite-size object
Small-angle scattering

9. Flux of particles The flux density The transfer equation
Mean free path, collision frequency, attenuation coefficient, optical depth