eqn_sheet

# eqn_sheet - EQUATION SHEET vP = x i y z k = vP et j = Re...

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E QUATION S HEET ! v P = " x ˆ i + " y ˆ j + " z ˆ k = v P ˆ e t = " R ˆ e R + R " ! ˆ e ! a P = "" x ˆ i + y ˆ j + z ˆ k = " v P ˆ e t + v P 2 ˆ e n = R " R " # 2 ( ) ˆ e R + R + 2 " R " ( ) ˆ e ! v B = ! v A + ! AB " ! r B / A = ! v A + ! v B / A ( ) rel + ! " ! r B / A ! a B = ! a A + ! AB " ! r B / A + ! AB " ! AB " ! r B / A ( ) = ! a A + ! a B / A ( ) rel + ! " ! r B / A + 2 ! " ! v B / A ( ) rel + ! " ! " ! r B / A ( ) dv dt = v dv ds ! = d ! " dt d ˆ e dt = ! " ˆ e ! F ! = m ! a G ; ! M A ! = I A ! + m ! r G / A # ! a A ; I A = mk A 2 = 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 tB ( ) ds 1 2 \$ + ! M B d ! % 1 2 \$ ! F ! ( ) ext dt 1 2 " = m ! v G 2 # m ! v G 1 ! M A ! ( ) ext dt 1 2 " = ! H A 2 # ! H A 1 ! H A = I A ! \$ ! H A = m ! r P / A % ! v P e = v Bn 2 ! v An 2 v An 1 ! v Bn 1 M !! x + C ! x + Kx = 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 Ccos d t + Ssin d t ( ) ; d = n ! 2 x P t ( ) = Acos t + Bsin t ; F t ( ) = F
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## This document was uploaded on 12/25/2011.

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