PHYS 326 :: Physics Illinois :: University of Illinois at Urbana-Champaign

Date    

Lecture

Readings

Homework Due

(instructions)

Thursday Problem Session

Tuesday Aug 25

L#1  Review Simple Harmonic Oscillator

T&M Chapter 3; Taylor Chapter 5; Approximate Lecture Notes (ALN) pp 1-8;

Relevant lectures from 325

Thursday Aug 27

L#2 linear 2-degree of freedom vibrations;

modes, eigenvalue problem

Taylor Chapter 11

T&M Chapter 12

ALN pp 7-12

Problem Session 1

solutions

Tuesday Sept  1

L#3  (weakly) coupled pendula, beats, loaded string 3dof

ALN   pp12-16

T&M §12.3   Taylor §11.3

HW 1 is due

solutionA   B

Thursday Sept 3

L#4 The Quadratic Lagrangian, MDoF vibrations

ALN 16-22  Taylor 441-444

T&M 475-481

Problem Session 2 Solution

Sunday Sept 6

Extra office hours .Loomis 322, 2 - 5 pm.

Monday Sept 7

 Labor Day (Loomis locked)

No office hours

Tuesday Sept 8

L#5 The linear algebra of the eigenmodes; orthonormality.

The modal matrix U

Thornton and Marion 481-483

ALN 23-28

HW 2 is due

Solution  A  B

Thursday Sept 10

L#6  The modal matrix U, degeneracy, coordinate changes,  normal coordinates, Symmetries

ALN  28-36

T&M  section 12.6

Taylor section 11.7

Problem session 3 solution

Tuesday Sept 15

L#7 Symmetries continued; Time-reversal non-invariance

ALN  36-43

HW 3   is due

solutionA,  B

Thursday Sept 17

L#8  Forced motions.

Green's Matrix

Problem session 4

solution

Tuesday Sept 22

L#9 Damped systems; undamped vibration absorber

Begin Nonlinear dynamics and chaos.  The logistic map.

Taylor 12.9

T&M 4.7

ALN 95-103

HW 4 is due

SolutionA;  B

Thursday Sept 24

L#10  fixed points of the logistic map, chaos, fractals, phase plane

Mathematica notebook

T&M 4.3, 4.4

ALN 104-114

Taylor 487-494

Session 5:

solution

Monday 9/29

regular office hours

Tuesday Sept 29

 L#11 , slides Numerical solutions of ODEs, driven damped pendulum

T&M 4.6

Taylor 12.2 – 12.8

ALN 114-129

No HW due

Wed Sept 30

Extra Office Hours

Loomis 322 1-2pm, 3-5pm.

Thursday Oct 1

 In-class midterm I Vibrations & modes

sample exam;   solution

Exam1 solution

lectures1-9, HW 1-4, Disc 1-4

Problem session 6

solution

Tuesday Oct 6

L#12 Begin rigid Body Dynamics

hw 5 python script (problems 1,2,3)

solution

T&M sections 1.4-1.7

Taylor 10.2-10.5

T&M 11.3-11.5

Taylor 10.8

T&M 11.9, 11.10

HW 5 due

solution A   B

mathematica sol A 

mathematica sol B

Thursday Oct 8

L#13. 

Inertia tensor for a rigid body

Taylor 10.9, 10.10

T&M  11.8, 11.10

Disc07

solution

Tuesday Oct  13

L#14  parallel axis theorem; Euler's equations

HW6 due

HW6Asolution

HW6Bsolution

Thursday Oct 15

L#15 Rotation matrices; Euler angles

Disc08

solution 1

solution 2

Tuesday Oct 20

L#16 Rotation matrices; Euler angles

Taylor 10.10,   T&M 11.11

HW7 due

solution  A

B

Thursday Oct 22

L#17. Dynamics of the top, precession, nutation.  Begin Hamiltonian Eqns.

Disc09

solution

Tuesday Oct 27

L#18.  Hamiltonian systems, Poisson brackets

Taylor Chpt 13, T&M 7.10-7.12

HW8 due

solutionA;  B

Thursday Oct 29

 L#19  Begin Continuum Mechs: Waves in strings

T&M 13.1 -13.8

Taylor 16.1 16.2

Disc10

solution

Tuesday Nov 3

L#20  Other 1-d systems; dispersion, boundaries & eigenfunctions, 

HW9 due

HW9Asolution

9Bsolution

sample exam

Wednesday Nov 4

Th Nov 5

L#21 Other 1-d systems: beams, hanging chain …modes, buckling, orthogonality, 

Disc11

solution

Monday 9 Nov

 office hours as usual

Tuesday Nov 10

in-class

midterm II today

Lectures 9  (from page 8 of the notes)– Lecture 18 (all of lecture 18, from the notes above)

MIDTERM II soln

sample exam

solution

No HW due

Thursday Nov  12

 L#22 

Energy, Greens function; Two-dimensions:  membranes; 

Discussion 12   soln

Tuesday Nov 17

 L#23 Two-dimensions:  membranes; 3D cwaves.

Taylor 16.4-16.7

HW10 due

solutionA,  B

Thursday Nov 19

 L#24  Stress, strain, moduli, stress and strain tensors, Hooke's law 

Taylor 16.10, 16.11

Disc 13

soln 

Week of Nov 22

FALL BREAK

Tuesday Dec 1

L#25 Hooke's law  and Elastic waves.

Taylor section 16.12

HW11 due

solutionA,   B

Thursday Dec 3

L#26  Begin Fluids

D/Dt,   acoustics, Bernouilli Eqn 

Disc 14

Tuesday Dec 8

L#27

Viscous laminar flows, Couette,

Sample Final Exam

HW 12 due

solutionA&B

Thursday Dec 10

 Extra office hours

 Loomis 251 1 - 4pm