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 = Tuesday nB LECTURE #2 = Thursday nd DISCUSSION = Thursday 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 8/28 1A - coupled oscillators → eigenmodes - weak-coupling demo R 8/30 1B - massless couplings: springs in series & parallel - math: proof of the det=0 technique - normal coordinates: easy case with 1 <-> 2 symmetry R 8/30 1d - weak-coupling demo part 1: practicing our new techniques ============================================================================ 2read T:11.3-5; M:4.5 T 9/4 2A - general formalism for small oscillations R 9/6 2B - "reading" the M and K matrices from T & U - good technique: the double pendulum R 9/6 2d - weak-coupling demo part 2: beats ============================================================================ 3read T:11.6-7 T 9/11 3A - DC modes - transverse oscillations of taut, loaded string R 9/13 3B - catalogue of modes in 3D - math: linear vector spaces & inner product spaces - normal modes as a linear vector space: statement R 9/13 3d - DC modes and the vibrations of the C02 molecule ============================================================================ 4read T:11.6-7 T 9/18 4A - normal modes as a linear vector space: proof - normal coordinates: general case R 9/20 4B - transformation rules for vectors and tensors - geometry of normal-coordinate space → dual basis R 9/20 4d - degenerate eigenvalues ============================================================================ 5read T:8.1-4 T 9/25 5A - diagonalization of M and K matrices - example 1: working in normal-coordinate space R 9/27 5B - [end of LinOsc] example 2: driven coupled oscillators +--------------------------------------------------------------+ | 2-BODY CENTRAL FORCE SYSTEMS & SCATTERING | +--------------------------------------------------------------+ R 9/27 5d - reduction to 1-body problem - calculating apsidal points ============================================================================ 6read T:8.5-8 T 10/2 6A - bounded and unbounded orbits - path equation : derivation - path equation : example R 10/4 6B - conic sections - bounded Kepler orbits & derivation of Kepler's Laws - motion of the individual particles ("wobble"/recoil) R 10/4 6d - Kepler orbit practice ============================================================================ 7read T:14.1-6 T 10/9 7A - scattering : capture cross sections - scattering : solid angle - scattering : differential cross sections - scattering : unbounded Kepler orbits & repulsive forces - scattering : hyperbola anatomy 1 R 10/11 7B <<<<< MIDTERM 1 : LINEAR OSCILLATIONS >>>>> R 10/11 7d - scattering : captured paths - Hohmann transfer orbits ============================================================================ 8read T:10.2-5; M:9.1-4 (Morin is particularly good on this topic) T 10/16 8A - scattering : hyperbola anatomy 2 - scattering : luminosity & rate +--------------------------------------------------------------+ | THE INERTIA TENSOR & EULER'S EQUATIONS | +--------------------------------------------------------------+ - the inertia tensor R 10/18 8B - principal axes of rotation - parallel-axis theorem & KE formula with inertia tensor - example: obtaining torque given constant rotation (and v.v.) R 10/18 8d - scattering : Rutherford cross section ============================================================================ 9read T:10.6-8; M:9.1,3-7,10 T 10/23 9A - tons of excellent questions :-) - example: obtaining motion immediately after an impulse R 10/25 9B - discussion of reference points - Euler's equations R 10/25 9d - inertia tensor: symmetries - inertia tensor: degenerate eigenvalues ============================================================================ T 10/30 10A - rotational stability - free symmetric top (FST) part 1 R 11/1 10B - FST part 2 R 11/1 10d - rotational trajectories - small oscillations from Euler's equations ============================================================================ T 11/6 11A - addition of angular velocities - Euler angles 1 +--------------------------------------------------------------+ | INTRODUCTION TO GENERAL RELATIVITY | +--------------------------------------------------------------+ 11read free chapters from Taylor & Wheeler R 11/8 11B - Chandler wobble - GR: the equivalence principle - GR: the bending of light - GR: gravitational redshift & time-dilation - GR: curved space-time R 11/8 11d - Euler angle practice - spinning top in gravity ============================================================================ T 11/13 12A - GR: the Schwarzschild metric R 11/15 12B - GR: natural units - GR: the metric tensor - GR: local flatness - GR: recovering special relativity - GR: local time measurements R 11/15 12d - GR: the GPS system ============================================================================ 11/17-11/25 FALL BREAK. HAPPY THANKSGIVING! ============================================================================ T 11/27 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 R 11/29 13B <<<<< MIDTERM 2 = central forces & rotations >>>>> R 11/29 13d - GR: curvature and reduced circumference ============================================================================ +--------------------------------------------------------------+ | CONTINUOUS MEDIA | +--------------------------------------------------------------+ 14read T:16.1-11 T 12/4 14A - transverse waves on a string: discrete → continuous - the 3D wave equation - waves on a finite string: boundary conditions & Fourier series R 12/6 14B - start continuum mechanics in solids - volume and surface forces - elastic moduli, stress, and strain - the stress tensor R 12/6 14d - wave practice ============================================================================ 15read T:16.3-11 T 12/11 15A - tension in massive strings - the strain tensor - generalized Hooke's Law - the Maxwell stress tensor from E&M ============================================================================ 16 <<<<< FINAL EXAM: Wednesday, December 19, 8:00am - 11:00am >>>>> <<<<< room: Loomis 143/144 >>>>> • 326 Course Explorer pageRegistrar's Final Exam site