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
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3. A proposed space station is
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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 xed orientation. (b) The period of the precession if the spin axis makes an angle of 20 with respect to the axis of xed 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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This note was uploaded on 11/08/2011 for the course AERO 16.61 taught by Professor Earlmurman during the Spring '03 term at MIT.

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hw10_ocw - closely approximated by four uniform spherical...

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