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hw10_ocw - closely approximated by four uniform spherical...

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16.61 Handout #10 Prof. J. P. How May 1, 2003 Prof. J. Deyst Due: May 8, 2003 16.61 Homework Assignment #10 1. Assume that a satellite can be modeled as a homogeneous cylinder shown below with a mass M = 200kg, axial moment of inertia 5M (kg-m 2 ) and transverse moment of inertia 20M (kg-m 2 ). Initially the ( force free ) satellite is moving such that the component of angular velocity i ω R parallel to the body axis of symmetry is 15 rev/hr and the nutation angle is 30 . Given this information, determine the following: (a) H 3 , H T , and the total magnitude of H (b) The precession rate and the spin rate. (c) The magnitude of i ω R (d) The body cone and space cone angles. (e) Sketch the body and space cones for this system. In your sketch include i ω R , H , and the axis of symmetry of the satellite. 2. Consider a paddle-wheeler steam boat moving forward downstream on the Mississippi River. The captain has commanded a very sharp turn to the left to avoid the other boat. What direction does the boat lean (in roll) as a result of the gyroscopic effects of the paddle-wheel? 1
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3. A proposed space station
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Unformatted text preview: closely approximated by four uniform spherical shells, each of mass m and radius r . The mass of the connection structure and internal equipment can be neglected. Station designed to rotate about its z-axis once every 4 sec, determine: (a) The number n of complete cycles of precession for each revolution about the z-axis if the plane of rotation deviates only slightly from a fixed orientation. (b) The period τ of the precession if the spin axis makes an angle of 20 ◦ with respect to the axis of fixed orientation about which the precession occurs. (c) Draw the space/body cones for the condition in part (b). 4. Do problem 18.84 from Beer and Johnston Vector Mechanics for Engineers . 2...
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