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!

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

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

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

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

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

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)

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

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