Problem 7.4 For the simplified model of Chelomei’s pendulum in Fig. P7.4:
(a) Set up the equations of motion for the case where horizontal oscillations of the
support Z h t
ð Þ ¼ Q h sin ð ~
Xt þ gÞ appear in addition to the vertical oscillations
Z v t
ð Þ ¼ Q v sinð ~
XtÞ.
(b) Using the method of direct separation of motions, consider the existence and
stability of a state where the rod performs small amplitude vibrations near
h = 0, while the disk performs small amplitude vibrations near a fixed value of
U 2 ]0;l[.
Fig. P7.3
Fig. P7.4
7.9 Problems
445
(a) Set up the equations of motion for the case where horizontal oscillations of the
support Z h t
ð Þ ¼ Q h sin ð ~
Xt þ gÞ appear in addition to the vertical oscillations
Z v t
ð Þ ¼ Q v sinð ~
XtÞ.
(b) Using the method of direct separation of motions, consider the existence and
stability of a state where the rod performs small amplitude vibrations near
h = 0, while the disk performs small amplitude vibrations near a fixed value of
U 2 ]0;l[.
Fig. P7.3
Fig. P7.4
7.9 Problems
445