MAT 272

Calculus and Analytic Geometry III

Fall 1997

 

Project 3: Tasks for final week

 

 

Refer to the MAPLE worksheet fallcat3.mws for common notation, and the correct equation of motion.

for any closed curve C in the "shape space" (xy-plane or q1q2-plane)?

Aside: Being not conservative is essentially the same as being controllable in the technical sense of geometric control theory. In this case controllable means that even though one has direct control of only q1(t) and q2(t), indirectly one can independently control all three states q1(t), q2(t), and a(t) by a judicious choice of the controls u1=(dq1/dt) and u2=(dq2/dt) think again of the motor-speeds in the "WORKING MODEL".--- Also, look in the article by Brockett in the NRC publication for a discussion of control systems of the form (dx/dt)=u1, (dy/dt)=u2, (dz/dt)=M(x,y)u1+N(x,y)u2 (you can't miss it, it is easy to find!)

 

New restriction: Assume that each joint allows only angles between (-3p/2) and (3p/2), i.e no full rotation (or twist of the cat).

 

 

Additional resource available:
Launch MATLAB on the CC_server, and type fallcat (followed by ENTER). Use the mouse to draw a polygonal path, and watch the results. You may replay the animation using the movie command. (type "help movie" and "help who" to get started).

 

Due date: Saturday, Dec 13 (Day of final exam). Corrections and "beautifications" will be accepted until Wednesday, Dec 17.

Deliverables: A well organized report that addresses all the items listed above in addition to the (corrected) items that were part of the first week's tasks. The report is NOT expected to be type-written, but must be of professional appearance (as standard in math, not in engineering, i.e. handwritten is OK!).
Summaries suitable for publication on the WWW and/or 11"x17" poster will earn bonus credit but please clear these with the instructor for technical soundness before finishing them. Last possible submission date for these is Wed Dec 17.