749_Dynamics 11ed Manual

749_Dynamics 11ed - I x I y I z to be constant This yields Σ M x I x x I y z y − I z y z = One can obtain y and z components in a similar manner

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Engineering Mechanics - Dynamics Chapter 21 For constant inertia, expanding the time derivative of the above equation yields Σ M x I x ω ' x I xy ' y I xz ' z () Ω z I y y I yz z I yx x () y I z z I zx x I zy y () + ... = One can obtain y and z components in a similar manner. Problem 21-41 Derive the Euler equations of motion for Ω ω i.e., Eqs. 21-26. 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 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 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 = Set I xy I yz = I zx = 0 = and require
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Unformatted text preview: I x I y , I z , to be constant. This yields Σ M x I x ' x I y z y − I z y z + = One can obtain y and z components in a similar manner. Problem 21-42 The flywheel (disk of mass M ) is mounted a distance d off its true center at G . If the shaft is rotating at constant speed , determine the maximum reactions exerted on the journal bearings at A and B . 747...
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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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