ExercisesWk5

ExercisesWk5 - CDS 140b Introduction to Dynamics Eva Kanso,...

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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 solid-fluid 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 body-fixed 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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ExercisesWk5 - CDS 140b Introduction to Dynamics Eva Kanso,...

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