Pendulums_all - (1 EGM 3400/3401 Classic pendulum dynamics example problems(2 Based on Chapter 19 in textbook(3 Example 1 Particle with 1 DOF(4

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Sheet1 Page 1 (1) % EGM 3400/3401 Classic pendulum dynamics example problems (2) % Based on Chapter 19 in textbook (3) % Example 1: Particle with 1 DOF (4) % Example 2: Rod with 1 DOF (5) % Example 3: Rod with 2 DOFs (6) Overwrite On (7) Frames N % n1> to the right, n2> up, and n3> = n1> x n2> (8) Points Q (9) Particles P (10) Bodies B (11) Variables theta'',Ten,Fx,Fy,x'' (12) Mass B=m,P=m (13) Inertia B,Ixx,Iyy,Izz,0,0,0 -> (14) I_B_BO>> = Ixx*B1>*B1> + Iyy*B2>*B2> + Izz*B3>*B3> (15) Constants g,l (16) % Rotation matrices (17) Simprot(N,B,3,theta) -> (18) N_B = [COS(theta), -SIN(theta), 0 (19) % Angular velocities (20) w_B_N>=theta'*b3> -> (21) w_B_N> = theta'*B3> (22) % Example 1: Particle with 1 DOF (23) % Linear velocities (24) v_No_N>=0> -> (25) v_No_N> = 0> (26) p_No_P>=-l*b2> -> (27) p_No_P> = -l*B2> (28) v_P_N>=v_No_N>+Cross(w_B_N>,p_No_P>) -> (29) v_P_N> = l*theta'*B1> (30) % Tension and gravity forces on P (31) F_P>=Ten*b2>-m*g*n2> -> (32) F_P> = Ten*B2> - g*m*N2> (33) F_P>=Express(F_P>,B) -> (34) F_P> = -g*m*SIN(theta)*B1> + (Ten-g*m*COS(theta))*B2> (35) M_B_P>=0> -> (36) M_B_P> = 0> (37) M_B_No>=Cross(p_No_P>,F_P>) -> (38) M_B_No> = -g*l*m*SIN(theta)*B3> (39) % Linear momentum principle (40) L_P_N>=m*v_P_N> -> (41) L_P_N> = l*m*theta'*B1>
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Sheet1 Page 2 (42) Zero_Lin>=F_P>-Dt(L_P_N>,N) -> (43) Zero_Lin> = -m*(g*SIN(theta)+l*theta'')*B1> + (Ten-g*m*COS(theta)-l*m* theta'^2)*B2> (44) EqnLin1=Dot(Zero_Lin>,n1>) -> (45) EqnLin1 = -SIN(theta)*(Ten-l*m*theta'^2) - l*m*COS(theta)*theta'' (46) EqnLin2=Dot(Zero_Lin>,n2>) -> (47) EqnLin2 = COS(theta)*(Ten-l*m*theta'^2) - g*m - l*m*SIN(theta)*theta'' (48) EqnLin3=Dot(Zero_Lin>,b1>) -> (49) EqnLin3 = -m*(g*SIN(theta)+l*theta'') (50) EqnLin4=Dot(Zero_Lin>,b2>)
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This note was uploaded on 06/13/2011 for the course EGM 3400 taught by Professor Matthews during the Spring '08 term at University of Florida.

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Pendulums_all - (1 EGM 3400/3401 Classic pendulum dynamics example problems(2 Based on Chapter 19 in textbook(3 Example 1 Particle with 1 DOF(4

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