**Readings and Homework, Fall 2018
ME 4730/5730, Dynamics
**

---- SUBJECT TO CHANGE, all semester long ----

---- This page in progress on 10/28/2018 ----

**Please read the Homework policy** a
few times, once before doing each of the first few homework assignments.

Assignments will be posted on Piazza.

**Homework Solutions:** TBD

Dynamics:Basic mechanics of 2D mechanisms by Newton-Euler, Lagrange or DAEs. Theory and practice

Basics:Ruina & Pratap (RP)The whole book (mostly review, but you shouldall of it).master

Topicswhich go a bit beyond many of the standard books

1)UsingMatlabfor simulations, plotting and animation.

2)Use ofAngular Momentum balanceto get equations of motion for complex systems.

3) Mechanisms(linked rigid objects)

4) DAE(Differential Algebraic Equations) formulation of equations of motion

3D Dynamics: We will cover the core ideas of the 3D dynamics of a single rigid object.

## Lecture schedule (Fall 2018, approximate, to be updated, subject to change)

Homework is due the first Wednesday that is at least 6 days after the assigned date. It is subject to change until midnight on the end of Thursday 6 days before it is due.

1)Intro. Position, velocity and acceleration in cartesian and polar coordinates.

2)Rotation matrix and computer animation

3)Particle Dynamics

4)Linear and Angular momentum, and Kinetic Energy

5)

6)Power, work, energy, momentum, angular momentum. Potential energy and conservative forces.

7) Multi-particle systems, axioms of mechanics

8)Polar Coord, Angular Momentum and Energy

9)Center of mass simplifications for H and Kin En.

10)Rotation with zero angular momentum (videos).

11)Energy Theorems for particles

Introduction to kinematic constraints and DAEs,

12)

12)Constraint's cont'd, bead on wire. Pendulum examples.

13)Constraint's (cont'd)

14)Pendulum, cont'd

16)Rigid objects

17))Vibrating inverted pendulum cont'd), also with DAEs.

18)Inverted pendulum (cont'd)

19Inverted pendulum (cont'd), Double Pend

20)?

21)Double Pend

22)Double Pend

23)Double Pend

24)Double Pend, Braked car slides

25)Chaplygin Sleigh

26)Generalized forces and Lagrange eqs.

27Rolling.

28)Rotating frames, Frame derivative

29)Qdot formula and velocity and acceleration formulas

30 )Intro to 3D rigid objects. Dyads.Linear functions and tensors.

31)Euler's Them. Rotation tensor

32)Dyadic representation of rotation

33)Matrix represenation of rotation

34)Small rotation and angular velocity

35)Dynamics (finally) of rigid object.CoM and angular momentum

36)Moment of inertia

37)Euler's equations

38)Euler's equations, body-frame version.

39)Static and Dynamic Balance

40)Wobbling plate

41)Steady precession of axisymmetric object

Rolling disk (Euler's disk)42)

Final Project Presentation(TBD):pdf report + computer demo (sign up to be posted)

FINAL EXAM:Comprehensive, including Matlab. No notes, books or calculators.