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 ============================================================================ +--------------------------------------------------------------+ | DAMPED & DRIVEN LINEAR OSCILLATORS | +--------------------------------------------------------------+ W 1/21 1read T:5.1-4; M:4.1-3 1B - recap: complex numbers - damped oscillations 1d - recap: Lagrangian mechanics - recap: small oscillations - linear diff eq: superposition & complex solutions ============================================================================ M 1/26 2read T:5.5-6; M:4.4 2A - driven, damped oscillations W 1/28 2B - resonance - math: linear vector spaces 2d - critical damping ============================================================================ +--------------------------------------------------------------+ | COUPLED LINEAR OSCILLATORS | +--------------------------------------------------------------+ M 2/02 3read T:5.7-8, 11.1-3; M:4.5 3A - linear vector spaces & Fourier series - coupled oscillators: eigenmodes W 2/04 3B - massless couplings: springs in series & parallel - weak coupling: example & demo - normal coordinates: easy case with 1 <-> 2 symmetry 3d - weak-coupling demo part 1: practicing our new techniques ============================================================================ M 2/09 4read T:11.3-5; M:4.5 4A - general formalism for small oscillations with coupling - "reading" the M and K matrices from T & U W 2/11 4B - good technique: the double pendulum 4d - weak-coupling demo part 2: beats ============================================================================ M 2/16 5read T:11.6-7 5A - DC modes: triatomic linear molecule W 2/18 5B - review of weeks 1-5 - transverse oscillations of taut, loaded string 5d - Fourier solution of driven, damped oscillator F 2/20 <<<<< EXTRA OFFICE HOURS 4-7 pm, Loomis 464 >>>>> ============================================================================ M 2/23 6A <<<<< MIDTERM 1 = damped,driven,coupled linear osc >>>>> W 2/25 6B - catalogue of modes in 3D - normal modes as a linear vector space - normal coordinates: general case 6d - degenerate eigenvalues ============================================================================ M 3/02 7read T:8.1-4 7A - geometry of normal-coordinates space → dual basis - diagonalization of M and K matrices +--------------------------------------------------------------+ | 2-BODY CENTRAL FORCE SYSTEMS & SCATTERING | +--------------------------------------------------------------+ W 3/04 7B - reduction to 1-body problem - bounded and unbounded orbits 7d - calculating apsidal points ============================================================================ M 3/09 8read T:8.5-6 8A - conic sections - path equation W 3/11 8B - path equation example - bounded Kepler orbits & derivation of Kepler's Laws 8d - Kepler orbit practice ============================================================================ M 3/16 9read T:8.8; T:14.1-2 9A - motion of individual particles ("wobble"/recoil) - Hohmann transfer orbits W 3/18 9B - capture cross sections - elements of scattering: solid angle, luminosity, rate ============================================================================ M 3/24 SPRING BREAK ============================================================================ M 3/30 10read T:8.7; T:14.1-6 10A - differential cross sections - unbounded Kepler orbits & repulsive forces +--------------------------------------------------------------+ | INTRODUCTION TO GENERAL RELATIVITY | +--------------------------------------------------------------+ W 4/01 10read free chapters from Taylor & Wheeler 10B - GR: equivalence principle - GR: gravitational redshift & time-dilation - GR: curved spacetime 10d - Rutherford cross section ============================================================================ M 4/06 11A - GR: the Schwarzschild metric - GR: natural units - GR: local time measurements - GR: recovering special relativity W 4/08 11B - GR: the Schwarzschild Radius & black holes - GR: the Principle of Maximal Aging - GR: the GR Lagrangian 11d - GR: the GPS system ============================================================================ M 4/13 12A - GR: measuring curvature - GR: reduced circumference W 4/15 12B - GR: local and global coordinates - GR: the path of light +--------------------------------------------------------------+ | THE INERTIA TENSOR & EULER'S EQUATIONS | +--------------------------------------------------------------+ 12read T:10.2-5; M:9.1-4 (Morin is particularly good on this topic) - the inertia tensor - principal axes of rotation 12d - inertia tensor: intuition - inertia tensor: degenerate eigenvalues ============================================================================ M 4/20 13A <<<<< MIDTERM 2 = central forces and scattering >>>>> 13read T:10.5-8 W 4/22 13B - parallel-axis theorem & KE formula with inertia tensor - example: obtaining torque given spin vector (and vice versa) 13d - symmetry theorems for the inertia tensor ============================================================================ M 4/27 14read T:13.6-7; T:9.1,3-7,10 14A - example: obtaining motion immediately after an impulse - Euler's equations W 4/29 14B - rotational stability - free symmetric top (FST) 14d - rotational trajectories - small oscillations from Euler's equations ============================================================================ M 5/4 15read T:7.9; 9.2,8 15A - some insights - FST example: the Chandler Wobble W 5/6 15B * EXTRA: Noether's Theorem → symmetry and conservation 15d * EXTRA: Noether's Theorem examples ============================================================================ FINAL EXAM: FRIDAY, MAY 15, 8-11 am, Loomis 151 (see registrar's Final Exam site) Final Exam covers everything except Noether's Theorem