| 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 | |
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