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The cited chapter/section numbers are in the course textbook:
Williams, J. H., Jr. Fundamentals of Applied Dynamics. New York, NY: John Wiley and Sons, Inc., 2006. ISBN: 9780470133859.
Course readings.
| SES # |
TOPICS |
READINGS |
| I. Motion of a single particle |
| 1 |
Course information
Begin kinematics: frames of reference and frame notation
|
1 |
| 2 |
The "spider on a Frisbee" problem
Kinematics using first principles: "downconvert" to ground frame
|
3.1, 3.2 |
| 3 |
Pulley problem, angular velocity, magic formula |
3.3, beginning of 3.4
Handout: kinematics (PDF)
|
| 4 |
Magic and super-magic formulae |
3.4, 3.5 theory |
| 5 |
Super-magic formula, degrees of freedom, non-standard coordinates, kinematic constraints |
3.5 problems, 3.6 |
| II. 2D Motion of system of particles |
| 6 |
Single particle: momentum, Newton's laws, work-energy principle, collisions |
4.1, 4.2 |
| 7 |
Impulse, skier separation problem |
4.4
Handout: note on in-class problem — skier sliding on semicircular mountain (PDF)
|
| 8 |
Single particle: angular momentum, example problem
Two particles: dumbbell problem, torque
|
4.3, 6.1, 6-2.1 |
| 9 |
Dumbbell problem, multiple particle systems, rigid bodies, derivation of torque = I*alpha |
6.2 |
| 10 |
Three cases, rolling disc problem |
6-3.1, 6-3.2 (restrict to 2D, most of the material is 3D) |
| 11 |
Work-energy principle |
|
| 12 |
Exam 1 recap |
Handout: rigid body dynamics (PDF) |
| 13 |
Exam 1 |
|
| III. Introduction to Lagrangian dynamics |
| 14 |
Generalized coordinates, introduction to Lagrangian, example problem |
5-4.1, 5-5 (see equations alone), examples in 5-5 without generalized force calculations |
| 15 |
Lagrangian derivation |
5-4.3, 5-4.4 |
| 16 |
Generalized forces, double pendulum problem |
5-4.4, examples in 5-5, 6-5, 2D examples in 6-6 |
| 17 |
Example problem |
Examples in 5-5, 6-5, 2D examples in 6-6 |
| 18 |
Exam 2 recap
Inverted pendulum, phase plots
|
Handout: Lagrangian formulation (PDF) |
| 19 |
Exam 2 |
|
| 20 |
Helicopter dynamics |
|
| IV. Vibrations |
| 21 |
Single DOF system: equilibrium, linearization, stability analysis |
8-1, 8-3 introduction |
| 22 |
Free response of a damped oscillator |
8-3.1 |
| 23 |
Free response (cont.) |
8-3.1 |
| 24 |
Free response (cont.), forced response |
8-3.5
Handout: the behavior of dynamic systems (PDF)
|
| 25 |
Forced response (cont.), Bode plots
Putting it all together (free + forced)
|
|
| 26 |
Final exam review |
|
| 27 |
Final exam |
|