All materials are available from the top URL, http://courses.physics.illinois.edu/phys326/ i.e. homework & discussion problems & solutions, lecture blackboards, formula sheets, and INFO files. The ITEM column contains these entries for week n: nread READING for week n = sections from textbooks nA LECTURE #1 = Monday nB LECTURE #2 = Wednesday nd DISCUSSION = Wednesday The READING item gives textbook sections for each week where the letters mean: T Taylor = the required textbook M Morin = the recommended textbook [eBook @ UIUC Library, off-campus access needs VPN in Tunnel All mode] DATE ITEM CONTENT ============================================================================ +--------------------------------------------------------------+ | COUPLED LINEAR OSCILLATORS | +--------------------------------------------------------------+ 1read T:5.7-8, 11.1-3; M:4.5 T 1/16 1A - coupled oscillators → eigenmodes - weak-coupling demo W 1/17 1d - weak-coupling demo part 1: practicing our new techniques R 1/18 1B - massless couplings: springs in series & parallel - math: proof of the det=0 technique - normal coordinates: easy case with 1 <-> 2 symmetry ============================================================================ 2read T:11.3-5; M:4.5 T 1/23 2A - general formalism for small oscillations W 1/24 2d - weak-coupling demo part 2: beats R 1/25 2B - "reading" the M and K matrices from T & U - good technique: the double pendulum ============================================================================ 3read T:11.6-7 T 1/30 3A - DC modes - transverse oscillations of taut, loaded string W 1/31 3d - DC modes and the vibrations of the C02 molecule R 2/1 3B - catalogue of modes in 3D - math: linear vector spaces & inner product spaces - normal modes as a linear vector space: statement ============================================================================ 4read T:11.6-7 T 2/6 4A - normal modes as a linear vector space: proof - normal coordinates: general case W 2/7 4d - degenerate eigenvalues R 2/8 4B - transformation rules for vectors and tensors - geometry of normal-coordinate space → dual basis ============================================================================ 5read T:8.1-4 T 2/13 5A - diagonalization of M and K matrices - example 1: working in normal-coordinate space +--------------------------------------------------------------+ | 2-BODY CENTRAL FORCE SYSTEMS & SCATTERING | +--------------------------------------------------------------+ W 2/14 5d - reduction to 1-body problem - calculating apsidal points R 2/15 5B - [end of LinOsc] example 2: driven coupled oscillators ============================================================================ 6read T:8.5-8 T 2/20 6A - bounded and unbounded orbits - path equation : derivation - path equation : example W 2/21 6d - Kepler orbit practice R 2/22 6B - conic sections - bounded Kepler orbits & derivation of Kepler's Laws - motion of the individual particles ("wobble"/recoil) ============================================================================ 7read T:14.1-6 T 2/27 7A - scattering : capture cross sections - scattering : solid angle - scattering : differential cross sections - scattering : unbounded Kepler orbits & repulsive forces - scattering : hyperbola anatomy 1 W 2/28 7d - scattering : captured paths - Hohmann transfer orbits R 3/1 7B <<<<< MIDTERM 1 : LINEAR OSCILLATIONS >>>>> ============================================================================ 8read T:10.2-5; M:9.1-4 (Morin is particularly good on this topic) T 3/6 8A - scattering : hyperbola anatomy 2 - scattering : luminosity & rate +--------------------------------------------------------------+ | THE INERTIA TENSOR & EULER'S EQUATIONS | +--------------------------------------------------------------+ - the inertia tensor W 3/7 8d - scattering : Rutherford cross section R 3/8 8B - principal axes of rotation - parallel-axis theorem & KE formula with inertia tensor - example: obtaining torque given constant rotation (and v.v.) ============================================================================ 9read T:10.6-8; M:9.1,3-7,10 T 3/13 9A - tons of excellent questions :-) - example: obtaining motion immediately after an impulse W 3/14 9d - inertia tensor: symmetries - inertia tensor: degenerate eigenvalues R 3/15 9B - discussion of reference points - Euler's equations ============================================================================ 3/18-3/24 SPRING BREAK WOOO!!! ============================================================================ T 3/27 10A - rotational stability - free symmetric top (FST) part 1 W 3/28 10d - rotational trajectories - small oscillations from Euler's equations R 3/29 10B - FST part 2 ============================================================================ T 4/3 11A - addition of angular velocities - Euler angles 1 W 4/4 11d - Euler angle practice - spinning top in gravity +--------------------------------------------------------------+ | INTRODUCTION TO GENERAL RELATIVITY | +--------------------------------------------------------------+ 11read free chapters from Taylor & Wheeler R 4/5 11B - Chandler wobble - GR: the equivalence principle - GR: the bending of light - GR: gravitational redshift & time-dilation - GR: curved space-time ============================================================================ T 4/10 12A - GR: the Schwarzschild metric W 4/11 12d - GR: the GPS system R 4/12 12B - GR: natural units - GR: the metric tensor - GR: local flatness - GR: recovering special relativity - GR: local time measurements ============================================================================ T 4/17 13A - GR: Schwarzschild coordinates - GR: local distance measurements - GR: the Schwarzschild Radius & black holes - GR: the Principle of Maximal Aging - GR: the GR Lagrangian - GR: constants of motion W 4/18 13d - GR: curvature and reduced circumference R 4/19 13B <<<<< MIDTERM 2 = central forces & rotations >>>>> ============================================================================ 14read T:16.1-11 T 4/24 14A - transverse waves on a string: discrete → continuous - the 3D wave equation - waves on a finite string: boundary conditions & Fourier series W 4/25 14d - wave practice R 4/26 14B - start continuum mechanics in solids - volume and surface forces - elastic moduli, stress, and strain - the stress tensor ============================================================================ 15read T:16.3-11 T 5/1 15A - tension in massive strings - the strain tensor - generalized Hooke's Law - the Maxwell stress tensor from E&M W 5/2 15d - TBA ============================================================================