pivoted_rod

# pivoted_rod - pivoted_rod.nb 1 In[1:= Apply Clear...

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In[1]:= Apply Clear, Names "Global` * " ; Off General::spell ; Off General::spell1 ; Print "Kinematics" ; omega t = 0, 0, theta' t ; Print "angular velocity of RB: omega = ", omega t ; alpha t = 0, 0, theta'' t ; Print "angular acceleration of RB: alpha = ", alpha t ; xG = L 2 - D * Sin theta t ; yG = - L 2 - D * Cos theta t ; rG = xG, yG, 0 ; Print "position vector of G: rG = ", rG ; vG = D rG, t ; Print "velocity of G: vG = d rG dt = ", vG ; aG = D vG, t ; Print "acceleration of G: aG = d vG dt = ", Simplify aG ; Print "another way of calculating vG and aG" ; vG = Cross omega t , rG ; Print "vG = omega x rG = ", vG ; aG = Cross alpha t , rG - omega t .omega t * rG; Print "aG = alpha x rG - omega.omega rG = ", Simplify aG ; Print "Forces" ; FO = FOx, FOy, 0 ; Print "reaction force at pin joint O: FO = ", FO ; G = 0, - m g, 0 ; Print "gravitational force at G: G = ", G ; rGO = - rG; IG = m * L^2 12; Print "mass moment of inertia wrt G: IGz = ", IG ; IO = IG + m * L 2 - D ^2; Print "mass moment of inertia wrt O: IOz = IGz + m * L 2 - D ^2 = ", Simplify IO ; Print "Method I" ; eqI = Simplify IO * alpha t - Cross rG, G ; solutionI = Solve eqI 3 ä 0, theta'' t 1 ; Print "moment equation: IO alpha = sum M wrt O = rG x G" ; Print eqI 3 , " = 0" ; Print "Solution: theta'' t = ", theta'' t . Simplify solutionI ; Print "Method II" ; eqIIF = Simplify m * aG - FO + G ; Print "force equation: m aG = sum F = FO + G" ; Print "projection on x:" ; Print

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## This note was uploaded on 08/29/2011 for the course MECH 6420 taught by Professor Marghitu during the Summer '11 term at University of Florida.

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pivoted_rod - pivoted_rod.nb 1 In[1:= Apply Clear...

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