ENME664_February_8&10_2010

ENME664_February_8&10_2010 - Particle Kinematics...

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Particle Kinematics • Material from Sections 2.4 and 2.5 of Kane (1961) • Material from Chapter 2 of Greenwood (1988)
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Particle Velocity and Acceleration   '' ' ' ' 2 DD D RR R R R CC C D D D R R R R R R R R R C C C r   vv ω aa ω vr ωω r ' R R D C r D C and are points located on body CD R .
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Particle Velocity and Acceleration   '' ' ' DD RR R R CC D R R R R R C r   v ω ar ωω r ' R R D C r D C and are points fixed on rigid body CD R .
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Particle Velocity and Acceleration   '' ' ' ' ' ' 2 C DD D RR R R R R OO C C C DDD D D R R R RRR C C C C r   vv v ω aa a ω vr ωω r ' R R D C r D C and are points located on body , and point is fixed in CD R O R ' . O
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Particle Acceleration Particle Acceleration       '2 ' 2 ' ' '' ' 2 2 ' 2 2 2            r r r r r r aR R R O P P R RR O O P R O P P RR RR O OR R O rr d d d d dt dt dt dt ++ r O O’ P R ρ ω Greenwood, Equation (2.106), Section 2.9 R ' R
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Particle Acceleration ' R O E   /' / ' ' ' ' 2 PP P EP O R P O R E E R E R E R E OO O     Coriolis Force aa v r r  λ Q P k ' RE  k
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Example 1 ' R '' Assume are unit vectors fixed in A Assume are unit vectors fixed in B Determine & Determine & i i PP RR OS a b aa vv
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Example 1 ' R      '' ' 1 ' ' 11 12 3 1 2 3 1 3 ' 1 2 1 ' ' (sin cos ) cos cos sin 2 RR PP R OO BR B RB P R S R B B O dd r dt dt rr r -R r -R r dt dt d dt       vr b bb ba b b b b b b va b b b b av a ω v       ' ' ' ' 2 RB RB O R SS P P B RBB S S d dt   r ωω r a ω r
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Example 2 ' R Assume are unit vectors fixed in A Assume are unit vectors fixed in D Determine & Determine & i i CC AL OO a n vv aa
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