Page 431 - Dynamics of Mechanical Systems

0593_C11_fm Page 412 Monday, May 6, 2002 2:59 PM

412 Dynamics of Mechanical Systems

β β
1

FIGURE P11.11.4
A double-rod pendulum with a β
concentrated end mass and relative 2
orientation angles. P(M)
P11.11.5: Use the results of Problem P11.11.4 and Eq. (11.11.1) to evaluate the generalized
active forces F and F . Compare the results and analysis effort with those of Problem
β 1 β 2
P11.5.4.
P11.11.6: See Problem P11.5.5. Consider again the triple-rod pendulum with concentrated
end mass of Problem P11.5.5 and as shown again in Figure P11.11.6. Determine the
potential energy of the system using a horizontal line through the pin support O as the
reference.

θ
1

θ
2

FIGURE P11.11.6
A triple-rod pendulum with a θ 3
concentrated end mass. P(M)
P11.11.7: Repeat Problem P11.11.6 using a horizontal line that is 3 below the pin support
of O as the reference for the potential energy.
P11.11.8: Use the results of Problems P11.11.6 and P11.11.7 and Eq. (11.11.1) to evaluate
the generalized active forces and F , F , and F . Compare the results and analysis effort
θ 1 θ 2 θ 3
with those of Problem P11.5.5.
P11.11.9: See Problem P11.5.6. Consider still further the triple-rod pendulum with a con-
centrated end mass. Let the orientation of the rods be defined by the relative orientation
angles β , β , and β , as shown in Figure P11.11.9. Repeat Problems P11.11.6 and P11.11.7
2
1
3
finding the potential energies for the relative orientation angles.
P11.11.10: Use the results of Problem P11.11.9 and Eq. (11.11.1) to evaluate the generalized
active forces F , F , and F . Compare the results and analysis effort with those of Problem
β 1 β 2 β 3
P11.5.6.
P11.11.11: See Problem P11.6.3. Consider again the rod pendulum with spring attachment
of Problem P11.6.3 and as shown again in Figure P11.11.11. Use Eq. (11.11.10) to determine
the potential energy of the spring. Then, use Eq. (11.11.1) to determine the contribution
of the spring force to the generalized active force F . Compare the results and analysis
θ
effort with those of Problem P11.6.3.