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Unformatted text preview: CDS 140b Introduction to Dynamics Eva Kanso, kanso@usc.edu February 7, 2008 1 Hw problems 1. Consider a rigid body B submerged in an infinite volume of inviscid, incompressible fluid that is assumed to remain irrotational at all time. That is, the fluid velocity is given by u = where is solution to Laplaces equation = 0 subject to boundary conditions: n  B = normal velocity of body ,  = 0 The kinetic energy of the solidfluid system is: T = X i 1 2 ( T I + mV T V )  {z } T s : Kinetic Energy of the Solids + 1 2 Z F f u u dv  {z } T f : Kinetic Energy of Fluid where and V are the bodys angular and linear velocities expressed in bodyfixed frame (say, chosen to coincide with the bodys principal axis). (a) Show that can be written as in terms of velocity potentials i and i ( i = 1 , 2 , 3) = i V i + i i where i and i are solutions to Laplaces equations subject to properly chosen boundary conditions....
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This note was uploaded on 01/04/2012 for the course CDS 140b taught by Professor List during the Fall '10 term at Caltech.
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