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final_eqns

# final_eqns - EQUATION SHEET a P = i j k x y z vP = i j k x...

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E QUATION S HEET v P = ˙ x i + ˙ y j + ˙ z k = v P e t = ˙ R e R + R ˙ ! e v B = v A + AB " r B / A a B = a A + AB " r B / A # \$ AB 2 r B / A v B = v A + v B / A ( ) rel + " r B / A a B = a A + a B / A ( ) rel + " r B / A + 2 # " v B / A ( ) rel + " " r B / A ( ) = d " dt ; de dt = # e F ! = ma G ; M A ! = I A + mr G / A # a A I A = mk A 2 I A = I G + md 2 T 1 + V 1 + U 1 ! 2 ( nc ) = T 2 + V 2 T = 1 2 mv A 2 + 1 2 I A 2 V sp = 1 2 k # 2 V gr = mgh U 1 ! 2 ( nc ) = F B e t ( ) ds B 1 2 \$ + M d % 1 2 \$ F ! ( ) ext dt 1 2 " = mv ! ( ) 2 # mv ! ( ) 1 M A ! ( ) ext dt 1 2 " = H A 2 # H A 1 H A = r P / A \$ P ; H A = I A e = v Bn 2 # v An 2 v An 1 # v Bn 1 M ˙ ˙ x + C ˙ x + K x = F t ( ) ; ˙ ˙ x + 2 !" n ˙ x + n 2 x = F t ( ) / M x t ( ) = x C t ( ) + x P t ( ) x C t ( ) = e # n t C cos d t + S sin d t [ ] ; d = n # 2 x P t ( ) = A cos t + B sin t ; for F t ( ) = F 0 sin t G L I G = 1 12 mL 2 G r I G = 1 2 mr 2 a P = ˙ ˙ x i + ˙ ˙
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