the suspended points, the two elastic reeds will rotate
reversely the angles /1 and /2 around the axis OZ,
respectively.
The compound pendulum is made of the same material,
and kS1 and kS2 are respectively elastic coefficients of the
upper and lower reeds. The mass of inverse pendulum is
divided into two sections. One is the disc with the inner
diameter of flute, whose mass is m2, and the other is the
rest, whose mass is m3. The mass of the simple pendulum
is m1.
The corresponding Lagrange equation of compound
pendulum is
d
dt
@L
@ _xi
@L
@xi
¼ 0 ð1Þ
where L = T V is the Lagrange function, T and V are
respectively the kinetic energy and potential energy of
compound pendulum system, and xi(i = 1, 2) represent
the generalized coordinates, namely /1 and /2.
From Eq. (1), we can obtain two equations expressed as
following