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SlidingPendulum - EGM 3400/3401 Sliding pendulum dynamics...

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Sheet1 Page 1 % EGM 3400/3401 Sliding pendulum dynamics example problem % Based on Chapter 19 in textbook % The pendulum is modeled as a rod with 2 DOFs %-------------------------------------------------------------------- % Set up problem AutoOverwrite On NewtonianFrame N % Nx> to the right, Ny> up, and Nz> = Nx> x Ny> RigidBody B Point Q Constant m,r,l,g Variable x'',theta'',Fy %-------------------------------------------------------------------- % Rotation matrices B.RotateZ( N, theta ) % B rotates "about +z" in N by theta %-------------------------------------------------------------------- % Angular velocities w_B_N> = theta'*Bz> %-------------------------------------------------------------------- % Linear velocities v_No_N> = 0> p_No_Q> = x*Nx> v_Q_N> = Dt( p_No_Q>, N ) p_Q_Bo> = -0.5*l*By> v_Bo_N> = v_Q_N> + Cross( w_B_N>, p_Q_Bo> ) Express( v_Bo_N>, N ) %-------------------------------------------------------------------- % Reaction forces on Q and gravity force on Bo F_Q> = Fy*Ny> F_Bo> = -m*g*Ny> Express( p_Q_Bo>, N ) M_B_Q> = Cross( p_Q_Bo>, F_Bo> ) %-------------------------------------------------------------------- % Linear momentum principle for Nx> direction L_B_N> = m*v_Bo_N> D_L_B_N> = Dt( L_B_N>, N ) Zero_Lin> = F_Q> + F_Bo> - D_L_B_N> Zero[1] = Dot( Zero_Lin>, Nx> ) %--------------------------------------------------------------------
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