771_Dynamics 11ed Manual

771_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Engineering Mechanics - Dynamics Chapter 21 A x A y A z T M y M z Find A x A y , A z , T , M y , M z , () = A x A y A z T 0.0 93.2 57.1 47.1 lb = M y M z 0.00 0.00 lb ft = Problem 21-61 Show that the angular velocity of a body, in terms of Euler angles φ , θ and ψ may be expressed as ω = ( ' sin θ sin ψ + ' cos ) i + ( ' sin cos ' sin ) j + ( ' cos + ' ) k , where i , j , and k are directed along the x, y, z axes as shown in Fig. 21-15 d . Solution: From Fig. 21 - 15 b , due to rotation , the x, y, z components of ' are simply ' along z axis From Fig. 21 - 15 c , due to rotation , the x, y , z components of ' and ' are ' sin in the y direction, ' cos in the z direction, and ' in the x direction. Lastly, rotation , Fig 21 - 15 d , produces the final components which yields ω ' sin () sin () ' cos () + () i ' sin () cos () ' sin () () j + ' cos () ' + () k + = Q.E.D Problem 21-62 A thin rod is initially coincident with the Z axis when it is given three rotations defined by the Euler
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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.

Ask a homework question - tutors are online