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lecture+notes+18 - 14:440:222 Dynamics (Lecture Note #18)...

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14:440:222 Dynamics (Lecture Note #1 8 ) Instructor: Prof. Peng Song Rutgers University
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Today’s Lecture • Relative-Motion Analysis Using Rotating Axes
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The velocity at B is given as : (d r B /dt) = (d r A /dt) + (d r B/A /dt) or v B = v A + v B/A Relative Motion Analysis: Velocity v B/A = d r B/A /dt = ω × r B/A
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a B = a A + ( a B/A ) t +( a B/A ) n Relative Motion Analysis: Acceleration a B = a A + α× r B/A ω 2 r B/A
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Applications
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A B A B / r r r + = Rotating Frame Position Ω = angular velocity of the x,y,z frame, measured from the X,Y,Z frame
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Differentiation of moving axes i i j j j i Ω = = Ω = = ) ( ) ( dt d dt d dt d dt d θ j j i i × Ω = × Ω = dt d dt d
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dt d A B A B / r v v + = + + + = + + + = + = dt d y dt d x dt dy dt dx dt d y dt dy dt d x dt dx y x dt d dt d B B B B B B B B B B A B j i j i j j i i j i r ) ( / Velocity A B xyz A B B B xyz A B y x / / / ) ( ) ( ) ( r v j i v × Ω + = + × Ω + = xyz A B A B A B ) ( / / v r v v + × + =
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This document was uploaded on 10/31/2011 for the course ENG MECH 232 at Rutgers.

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lecture+notes+18 - 14:440:222 Dynamics (Lecture Note #18)...

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