Dynamics and control i

Lectures: 2 sessions / week, 1.5 hours / session

Recitations: 1 session / week, 1 hour / session

MATLAB® Sessions: 1 session / week, 1 hour / session

This version of the class stresses kinematics and builds around a strict but powerful approach to kinematic formulation which is different from the more traditional approach presented in Spring 2007.

Our notation was adapted from that of Professor Kane of Stanford University. We use strict frames, a strict notation for relative velocities and accelerations, frame-oriented derivates of vectors, and a constructive approach to the derivation of linear and angular velocities and accelerations.

Williams, J. H., Jr. Fundamentals of Applied Dynamics. New York, NY: John Wiley and Sons, Inc., 2006. ISBN: 9780470133859.

Meriam, J. L., and L. G. Kraige. Engineering Mechanics: Dynamics. 5th ed. Vol. 2. New York, NY: J. Wiley & Sons, 2001. ISBN: 9780471406457.

Each week, there will be two class lectures, one MATLAB® session, and one recitation.

There will be two types of problem sets, one for the dynamics part and one for the MATLAB part. Dynamics problem sets will typically be assigned on Mondays and due the next Monday. They are available in the assignments section. To receive credit, problem sets must be handed in at the beginning of class on the due date. Because of holidays, tests, etc., some problem sets may be provided and will be due on days other than Mondays for some weeks. For the same reason, they may not be assigned for a particular week. Late problem sets will not be accepted. MATLAB problem sets will be handed out during MATLAB sessions and will be due in class on the due-date.

You are welcome, and encouraged, to work on the assignment problems with fellow students. A good way to learn the material is in small study groups. Such groups work best if members have attempted the problems individually before meeting as a group. Of course, the assignment solution that you turn in should reflect your own understanding, and not that of your fellow students. In other words, do not copy directly from other students. If it is obvious that such direct copying has occurred, we will disallow that homework.

Homework and classwork include:

Kinematics: Frames, transforming between frames, derivatives of vectors, velocity, acceleration, angular velocity, angular acceleration, centripetal terms, Coriolis terms

Dynamics: Linear momentum principle, angular momentum principle for system of particles, 2D motion of rigid body: Momentum principles, inertia tensor, parallel axes theorem, instantaneous center of rotation, work-energy principle; variable mass systems

Generalized coordinates and forces; Lagrangian equations of motion for 2D holonomic systems of particles and rigid bodies. Helicopter dynamics

Phase plots, equilibria, linearization, stability. 1-DOF oscillations: natural frequencies, free-, damped-, and forced response; time response, frequency response, bode plots

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