# ps8 - horizontal surface can be modeled as viscous damping...

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1.053/2.003 Dynamics and Control I Fall 2007 Problem Set 8 Out: Tuesday, November 6 th , 2007 Due: Wednesday, November 14 th , 2007 1. Rack and pinion (Modified from Williams, Problem 6-109) A rack and pinion system is sketched in Figure P6-109. The axis of the pinion is fixed in frictionless bearings. A massless rocket is attached to the circular massless pulley of radius a at a point along its edge as shown in the figure. It exerts thrust F(t) which remains tangential to the pulley at all times. Assume that the pinion can be modeled as a uniform cylinder of mass m 2 and radius b and that the friction between the rack and the
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Unformatted text preview: horizontal surface can be modeled as viscous damping having a dashpot constant c . Derive the equation(s) of motion for the system using Lagrangian approach. 2. Problem 6-101 from Williams. 3. Problem 6-103 from Williams. 4. Problem 6-110 from Williams. Cite as: Sanjay Sarma, Nicholas Makris, Yahya Modarres-Sadeghi, and Peter So, course materials for 2.003J/1.053J Dynamics and Control I, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. k F ( t ) k Viscous damping, c Rack, m 1 Pinion, m 2 + b a Figure by MIT OpenCourseWare....
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