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# hw07 - a particular x,y coordinate c A particle moving in a...

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AE 352: Aerospace Dynamics II, Fall 2008 Homework 7 Due Friday, October 24 Problem 1. Write down the constraint equations for each of the following descrip- tions. Note that you must first identify the generalized coordinates. In your answer, also specify the number of degrees of freedom before and after the constraint, and whether the constraints are holonomic or nonholonomic. a) A particle is constrained to lie in a horizontal plane. b) A particle is attached to a massless inextensible rod in a vertical plane. The end of the rod opposite the mass is constrained to be attached to a pivot located at
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Unformatted text preview: a particular x,y coordinate. c) A particle moving in a vertical plane is constrained to be a distance l from the origin. d) A unicycle (thin disc of mass m ) is constrained to roll without slipping on a horizontal surface (ignore the z-direction, i.e. assume the disc is always in contact with a horizontal plane). Problem 2. Use Lagrange multipliers to ﬁnd the tension in the simple pendulum. Problem 3. Greenwood 6-14. Problem 4. Use Lagrange multipliers to ﬁnd the constraint forces in the system given in Greenwood Example 6-6. Page 1 of 1...
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