Readings

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.

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  

Learning Resource Types

theaters Lecture Videos
assignment Problem Sets
grading Exams
assignment_turned_in Programming Assignments with Examples
co_present Instructor Insights