differential_terms

# differential_terms - ME/ECE 739 Diﬀerential Motion...

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Unformatted text preview: ME/ECE 739 Diﬀerential Motion Equations - Professor Nicola J. Ferrier 1 ∂ 0T j ∂qi = D 0T i j 0 − 0T −1 D i j 0 Di Dj − Dj Di 0 Di 0P j 0 D D 0T k i j D D 0P k i j i≤j and i>j d( 0T ) j dt = Wj 0T j ∂ 0T −1 j ∂qi i≤j and i>j d( 0T −1 ) j dt = = − 0T −1 Wj j ∂Dj ∂qi i≤j and i>j dDj dt = = Wj−1 Dj − Dj Wj−1 ∂ 0P ∂ 0T jP j j = j ∂qi ∂qi i≤j and i>j d 0P j dt = = Wj 0P j ∂ 2 0T j ∂qk ∂qi k≤i≤j i≤k≤j i > j or k > j and 0 d2 jT dt2 = Di Dk T 0 0 j = (αj + Wj Wj ) 0T j ∂ 2 0P j ∂qk ∂qi k≤i≤j i≤k≤j i > j or k > j and 0 d2 jP dt2 = Di Dk 0P j 0 = (αj + Wj Wj ) 0P j where Di = and αN = i=1 0 i 1 − T Qi 0 i 1 − T −1 and Wj = j ˙ i=1 Di qi N [(Wi−1 Di − Di Wi−1 )qi + Di qi ] ˙ ¨ Recursive calculation Formulas Wj αj αj + Wj Wj = Wj−1 + Dj qj with W0 = 0 ˙ = αj−1 + Dj qj + (Wj−1 Dj − Dj Wj−1 ) qj with α0 = 0 ¨ ˙ = αj−1 + Wj−1 Wj−1 + Dj qj + 2Wj Dj qj + Dj Dj (qj )2 ¨ ˙ ˙ ...
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## This note was uploaded on 08/08/2008 for the course ME 739 taught by Professor Ferrier during the Spring '06 term at University of Wisconsin.

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