**Readings and Homework, Fall 2015
ME 4730/5730, Dynamics and Vibrations**

---- This page in progress on 9/17/2015 ----

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

**Homework assignments: ** pdf .
Updated 9/17/2015.

**Homework Solutions:** Will be posted on Piazza.

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) DAEf (Differential Algebraic Equations) formulation of equations of motion

Vibrations: We will cover most of the content of most elementary Vibrations books.

Forced, damped harmonic oscillator (inside and out).

Linearization, normal modes and damped normal modes, matrix exponential, structural vibrations.

## Lecture and homework schedule

1) August 26 WedIntro. Position, velocity and acceleration in cartesian and polar coordinates.

Topic:

Homework:1 (Read up), 2 (polar coordinates with force = zero).

2) August 29 FriNewtons laws and ballistics, various force laws

Topic:

Homework:3 (Canonball)

3) Aug 31 MonSolutions for famous particle dynamics problems.

Topic:

Homework:4 (Mass hangs from spring.), 5 (central force), 6 (canonball 2)

4) Septem 02 WedPower, work, energy, momentum, angular momentum

Topic:

Homework:7(what means rate of change of angular momentum?)

5) Septem 04 FriPotential energy and conservative forces.

Topic:

*** Monday is Labor Day ***

6) Septem 9 WedSummary of single particle mechanics, Multi-particle systems

Topic:

Homework:8 (2 or 3 particles in circular motion), 9 (Montgomery's 8),

7) Septem 11 FriThe axioms of mechanics, multi-particle systems

Topic:

Homework:10 (Konig's Theorem), 11 (Angular momentum for multiple particles)

8) Septem 14 MonMultiparticle systems, Momentum, Angular Momentum, Intro to cats

Topic:

9) Septem 16 WedMechanics summarized, Cats and Astronauts

Topic:

Homework:12 (rotation with zero angular momentum), 13 (two masses connected by a spring)

10) Septem 18 FriRotation with zero angular momentum (continued).

Topic:

11) Septem 21 Mon.Introduction to kinematic constraints and DAEs, bead on a curved wire.

Topic:

12) Septem 23 WedPendulum examples.

Topic:

13) Septem 25 FriPendulum (cont'd)

Topic:

14) Septem 28 Mon2D Angular velocity. Dynamics of one or more rigid objects in 2D (Lin Mom, Ang Mom, Kin Energy).

Topic:

15) Sept 30 WedVibrating inverted pendulum. Equivalence between gravity and accelerating reference frames.

Topic:

16) Octob 02 FriVibrating inverted pendulum ( cont'd), also with DAEs.

Topic:

Double pendulum (intro).

17) Octob 05 MonDouble pendulum (cont'd).

Topic:

18) Octob 07 WedDouble pendulum (cont'd).

Topic:

DAEs with multiple rigid objects.

Minimal and 'maximal' coordinates.

19) Octob 9 FriChaplygin Sleigh (grocery cart, braked car directional stability)

Topic:

*** Fall Break Mon and Tues ***

20) Octob 14 Wed.Lagrange Eqs., Matlab symbolics for Lagrange eqs.

Topic:

21) Octob 16 FriRotating frames, 5-term acceleration formula

Topic:

22) Octob 19 Mon5-term Acc formula continued

Topic:*** Prelim 1, Tuesday October 20, 7:30 - 9 (plus up to 90 minutes extra time ) ***

Covers through HW handed in by Oct 19, including Matlab.

23) Octob 21 WedExamples of 2D mechanisms and problems

Topic:

24) Octob 23 FriGeneralized forces and Lagrange eqs.

Topic:

25) Octob 26 MonDAEs for many bodies (cont'd). Rolling.

Topic:

26) Octob 28 WedIntro. to Vibrations, 1 DOFspring and mass.

Topic:

27) Octob 30 FriMore Single DOF vibrations: damping

Topic:

28) Novemb 02 MonSinusoidal forcing and resonance

Topic:

29) Novemb 04 WedLogarithmic decrement, measurement

Topic:

30) Novemb 06 Fri1 DoF review

Topic:

31) Novemb 9 MonMisc 1 DoF things: Friction, Superposition, Fourier Series

Topic:,Intro to multi-DOF vibrations

32) Novemb 11 Wed(class is held on Veterens day)Multi DoF (cont'd)

Topic:

33) Novemb 13 FriForcing and vibration absorption

Topic:

34) Novemb 16 MonNormal modes using Inv(M)

Topic:*** Prelim 2, Tuesday Nov 17, 7:30 - 9 (plus up to 90 minutes extra time) ***

Covers through HW handed in by Nov 17, including Matlab.

35) Novemb 18 Wed:Normal modes using sqrt(M)

Topic:

36) Novemb 20 FriState Space, Matrix exponential

Topic:

Matrix exponential (cont'd)

37) Novemb 23 Mon

Topic:

*** Thanksgiving starts Tuesday night ****

39) Nov. 30 MonNormal modes with damping

Topic:

40) Dec. 02 WedModal damping

Topic:

41) Dec. 04 FriStructural Vibrations (computer demo)

Topic:

Study Period:Saturday Dec 5 - Tuesday Dec 8

Final Project Due Dec 9, 4:30 PM(Univ. set date and time):pdf report + computer demo (sign up to be posted)

FINAL EXAM:Date, time and place to be determined (let me know when you find it, and I'll post it.)Comprehensive, including Matlab. No notes, books or calculators.