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 should master all of it).
Topics which go a bit beyond many of the standard books
1) Using Matlab for simulations, plotting and animation.
2) Use of Angular Momentum balance to 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
12) Introduction to kinematic constraints and DAEs,
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)
19 Inverted pendulum (cont'd), Double Pend
21) Double Pend
22) Double Pend
23) Double Pend
24) Double Pend, Braked car slides25) Chaplygin Sleigh
26) Generalized forces and Lagrange eqs.27 Rolling.
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 velocity35) 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
42) Rolling disk (Euler's disk)
Final Project Presentation (TBD): pdf report + computer demo (sign up to be posted)
Comprehensive, including Matlab. No notes, books or calculators.