748_Dynamics 11ed Manual

748_Dynamics 11ed Manual - x i y j + z k + = and expanding...

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Engineering Mechanics - Dynamics Chapter 21 Solution: In general M t H x i H y j + H z k + () d d = M H' x i H' y j + H' z k + () Ω H x i H y j + H z k + () × + = Substitute Ω Ω x i y j + z k + = and expanding the cross product yields M H' x z H y y H z + () i H' y x H z z H x + () j + H' z y H x x H y + () k + ... = Substitute H x , H y , and H z using Eq. 21 - 10. For the i component Σ M x t I x ω x I xy y I xz z () z I y y I yz z I yx x () y I z z I zx x I zy y () + ... d d = One can obtain y and z components in a similar manner. *Problem 21-40 Derive the scalar form of the rotational equation of motion along the x axis when Ω ω and the moments and products of inertia of the body are constant with respect to time. Solution: In general M t H x i H y j + H z k + () d d = M H' x i H' y j + H' z k + () Ω H x i H y j + H z k + () × + = Substitute
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Unformatted text preview: x i y j + z k + = and expanding the cross product yields M H' x z H y y H z + ( ) i H' y x H z z H x + ( ) j + H' z y H x x H y + ( ) k + ... = Substitute H x , H y , and H z using Eq. 21 - 10. For the i component M x t I x x I xy y I xz z ( ) z I y y I yz z I yx x ( ) y I z z I zx x I zy y ( ) + ... d d = 746...
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This note was uploaded on 08/16/2011 for the course EGN 3321 taught by Professor Christianfeldt during the Spring '08 term at University of Central Florida.

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