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 8/29 1A - coupled oscillators → eigenmodes - weak-coupling demo R 8/31 1B - massless couplings: springs in series & parallel - math: proof of the det=0 technique 1d - weak-coupling demo part 1: practicing our new techniques - normal coordinates: easy case with 1 <-> 2 symmetry ============================================================================ 2read T:11.3-5; M:4.5 T 9/5 2A - general formalism for small oscillations R 9/7 2B - "reading" the M and K matrices from T & U - good technique: the double pendulum 2d - weak-coupling demo part 2: beats ============================================================================ 3read T:11.6-7 T 9/12 3A - DC modes - transverse oscillations of taut, loaded string R 9/14 3B - catalogue of modes in 3D - math: linear vector spaces & inner product spaces - normal modes as a linear vector space: statement 3d - DC modes and the vibrations of the C02 molecule ============================================================================ 4read T:11.6-7 T 9/19 4A - normal modes as a linear vector space: proof - normal coordinates: general case R 9/21 4B - transformation rules for vectors and tensors - geometry of normal-coordinate space → dual basis 4d - degenerate eigenvalues ============================================================================ 5read T:8.1-4 T 9/26 5A - diagonalization of M and K matrices - example 1: working in normal-coordinate space +--------------------------------------------------------------+ | 2-BODY CENTRAL FORCE SYSTEMS & SCATTERING | +--------------------------------------------------------------+ R 9/28 5B - [end of LinOsc] example 2: driven coupled oscillators 5d - reduction to 1-body problem - calculating apsidal points ============================================================================ 6read T:8.5-8 T 10/3 6A - bounded and unbounded orbits - path equation : derivation - path equation : example R 10/5 6B - conic sections - bounded Kepler orbits & derivation of Kepler's Laws - motion of the individual particles ("wobble"/recoil) 6d - Kepler orbit practice ============================================================================ 7read T:14.1-6 T 10/10 7A - scattering : capture cross sections - scattering : solid angle - scattering : differential cross sections - scattering : unbounded Kepler orbits & repulsive forces - scattering : hyperbola anatomy 1 R 10/12 7B <<<<< MIDTERM 1 : LINEAR OSCILLATIONS >>>>> 7d - scattering : captured paths - Hohmann transfer orbits ============================================================================ 8read T:10.2-5; M:9.1-4 (Morin is particularly good on this topic) T 10/17 8A - scattering : hyperbola anatomy 2 - scattering : luminosity & rate +--------------------------------------------------------------+ | THE INERTIA TENSOR & EULER'S EQUATIONS | +--------------------------------------------------------------+ - the inertia tensor R 10/19 8B - principal axes of rotation - parallel-axis theorem & KE formula with inertia tensor - example: obtaining torque given constant rotation (and v.v.) 8d - scattering : Rutherford cross section ============================================================================ 9read T:10.6-8; M:9.1,3-7,10 T 10/24 9A - tons of excellent questions :-) - example: obtaining motion immediately after an impulse R 10/26 9B - discussion of reference points - Euler's equations 9d - inertia tensor: symmetries - inertia tensor: degenerate eigenvalues ============================================================================ T 10/31 10A - rotational stability - free symmetric top (FST) part 1 R 11/2 10B - FST part 2 10d - rotational trajectories - small oscillations from Euler's equations ============================================================================ T 11/7 11A - addition of angular velocities - Euler angles 1 R 11/9 11B - Chandler wobble 11d - Euler angle practice - spinning top in gravity ============================================================================ +--------------------------------------------------------------+ | INTRODUCTION TO GENERAL RELATIVITY | +--------------------------------------------------------------+ 12read free chapters from Taylor & Wheeler T 11/14 12A - GR: the equivalence principle - GR: the bending of light - GR: gravitational redshift R 11/16 12B - GR: gravitational time dilation - GR: curved space-time - GR: overview of key GR concepts - GR: the Minkowski metric of flat spacetime (SR review) - GR: the Schwarzschild metric 12d - GR: the GPS system ============================================================================ M 11/20 THANKSGIVING BREAK ============================================================================ T 11/28 13A - GR: metric of a spherical surface &rarr local flatness - GR: natural units - GR: the Schwarzschild radius - GR: black holes - GR: special relativity embedded in general relativity R 11/30 13B <<<<< MIDTERM 2 = central forces & rotations >>>>> 13d - GR: curvature ============================================================================ T 12/5 14A - GR: significance of proper time & distance (SR review) - GR: local time measurements - GR: Lorentz time dilation from the metric - GR: gravitational time dilation from the metric R 12/7 14B - GR: analysis of grav time dilation thought experiment - GR: position & time "over there" → grid of rods & clocks - GR: meaning of "faraway" Schwarzschild coordinates 14d - GR: reduced circumference and the "Funnel Figure" ============================================================================ T 12/12 15A - GR: local distance measurements - GR: reduced circumference and the "Funnel Figure" - GR: the Principle of Maximal Aging - GR: the GR Lagrangian - GR: constants of motion - GR: form of gravitational force from Schwarzschild metric ============================================================================ 16 <<<<< FINAL EXAM: Monday Dec 18, 8:00 am - 11:00 am >>>>> <<<<< rooms: 139, 143, 144 Loomis >>>>> • 326 Course Explorer page • Registrar's Final Exam site