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 1/19 1A - coupled oscillators → eigenmodes - weak-coupling demo W 1/20 1d - weak-coupling demo part 1: practicing our new techniques R 1/21 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 1/26 2A - general formalism for small oscillations W 1/27 2d - weak-coupling demo part 2: beats R 1/28 2B - "reading" the M and K matrices from T & U - good technique: the double pendulum ============================================================================ 3read T:11.6-7 T 2/2 3A - DC modes - transverse oscillations of taut, loaded string W 2/3 3d - DC modes and the vibrations of the C02 molecule R 2/4 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 2/9 4A - normal modes as a linear vector space: proof - normal coordinates: general case - geometry of normal-coordinates space → dual basis W 2/10 4d - degenerate eigenvalues R 2/11 4B - diagonalization of M and K matrices - driven coupled oscillators - mode energy F 2/12 <<<<< EXTRA OFFICE HOURS 5-8 pm, Loomis 464 >>>>> ============================================================================ +--------------------------------------------------------------+ | 2-BODY CENTRAL FORCE SYSTEMS & SCATTERING | +--------------------------------------------------------------+ 5read T:8.1-4 T 2/16 5A - reduction to 1-body problem - bounded and unbounded orbits T 2/16 <<<<< OFFICE HOURS moved from Thu to Tue, 4-7 pm, Loomis 464 W 2/17 5d - calculating apsidal points R 2/18 5B <<<<< MIDTERM 1 : LINEAR OSCILLATIONS >>>>> ============================================================================ 6read T:8.5-6 T 2/23 6A - path equation : derivation - path equation : example W 2/24 6d - Kepler orbit practice R 2/25 6B - conic sections - bounded Kepler orbits & derivation of Kepler's Laws ============================================================================ 7read T:8.7-8; T:14.1-6 T 3/1 7A - motion of the individual particles ("wobble"/recoil) - scattering : capture cross sections W 3/2 7d - scattering : captured paths - Hohmann transfer orbits R 3/3 7B - scattering : solid angle - scattering : differential cross sections - scattering : unbounded Kepler orbits & repulsive forces - scattering : hyperbola anatomy 1 ============================================================================ 8read T:10.2-5; M:9.1-4 (Morin is particularly good on this topic) T 3/8 8A - scattering : hyperbola anatomy 2 - scattering : luminosity & rate +--------------------------------------------------------------+ | THE INERTIA TENSOR & EULER'S EQUATIONS | +--------------------------------------------------------------+ - the inertia tensor W 3/9 8d - scattering : Rutherford cross section R 3/10 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 3/15 9A - tons of excellent questions :-) - example: obtaining motion immediately after an impulse W 3/16 9d - inertia tensor: symmetries - inertia tensor: degenerate eigenvalues R 3/17 9B - discussion of reference points - Euler's equations ============================================================================ M 3/21 SPRING BREAK ============================================================================ T 3/29 10A - rotational stability - free symmetric top (FST) part 1 W 3/30 10d - rotational trajectories - small oscillations from Euler's equations R 3/31 10B - FST part 2 - Chandler wobble - addition of angular velocities ============================================================================ R 4/5 11A - Euler angles +--------------------------------------------------------------+ | INTRODUCTION TO GENERAL RELATIVITY | +--------------------------------------------------------------+ 11read free chapters from Taylor & Wheeler - GR: the equivalence principle W 4/6 11d - Euler angle practice - spinning top in gravity R 4/7 11B - GR: the bending of light - GR: gravitational redshift & time-dilation - GR: curved space-time ============================================================================ T 4/12 12A - GR: the Schwarzschild metric - GR: natural units - GR: local time measurements - GR: recovering special relativity - GR: Schwarzschild coordinates T 4/12 <<<<< OFFICE HOURS moved from Thu to Tue, 4-7 pm, Loomis 464 W 4/13 12d - GR: the GPS system R 4/14 12B <<<<< MIDTERM 2 = central forces & inertia tensor >>>>> ============================================================================ T 4/19 13A - GR: the Schwarzschild Radius & black holes - GR: the Principle of Maximal Aging - GR: the GR Lagrangian - GR: local distance measurements W 4/20 13d - GR: curvature and reduced circumference +--------------------------------------------------------------+ | CONTINUUM MECHANICS | +--------------------------------------------------------------+ 13read T:16.1-2 R 4/21 13B - GR: constants of motion - transverse waves on a string: discrete → continuous ============================================================================ 14read T:16.3-11 T 4/26 14A - the 3D wave equation - waves on a finite string: boundary conditions & Fourier series W 4/27 14d - wave practice R 4/28 14B - start continuum mechanics in solids - volume and surface forces - elastic moduli, stress, and strain - the stress tensor ============================================================================ 15read T:16.3-11 T 5/3 15A - tension in massive strings - the strain tensor - generalized Hooke's Law - the Maxwell stress tensor from E&M T 5/3 <<<<< OFFICE HOURS moved from Thu to Tue, 4-7 pm, Loomis 464 W 5/4 15d - TBD ============================================================================ 16 T 5/10 <<<<< OFFICE HOURS moved from Thu to Tue, 4-7 pm, Loomis 464 W 5/11 <<<<< FINAL EXAM, 8 - 11 am, Loomis 151 >>>>> ============================================================================ FINAL EXAM: WEDNESDAY, MAY 11, 8-11 am, Loomis 151 (see registrar's Final Exam site or click the Show Final Exam Schedule button on the 326 Catalog page)