A MONOPOD GRAVITY PLATFORM
235
of the structure^ independent coordinates £, = v and
= G. or
d dK
dK
dV
dt di)
dv + dv~9v
(9.37)
d dK
dK
dV
dt dG ’ dG + 'dG="
(9.38)
The kinetic energy K, the potential energy V, and the nonconservative Virtual
work <5W of the system’s nonconservative generalized forces gv and ge are, respectively,
K = - m(v + hGG)2 + | JGd2
(9.39)
V = -fcii»2 +
~
~ cosG) + mbghb(l — cosG)
(9.40)
SW — gvSv + ggSG = [—ciû + F]<5v + [—cgi) + HqF -I- Mp^SG
(9-41)
When the last three équations are used with équations (9.37), and then with
(9.38), the respective équations for plane motion become
mv + mhG0 + Civ + kiv = F
(9.42)
mhGï> + ( JG + mhG)G + cgG + (fc« - TnoghG + mbghb)G = h0F + Mpc (9.43)
The above two équations can be written in standard form in the following way:
Multiply équation (9.42) by (~hG) and add this resuit to équation (9.43) to
give
JgG + cgG — hGcii) + (kg — moghG + mbghbjG — hGk^v = Mpc + (ho — hG)F
(9.44)
Then substitute G from this resuit into équation (9.42). Thus
mv + — ciû — m^GCgG----- — mophc + mbghb)G 4- — kiv
Jg
Jg
Jg
Jg
= £_^(/l0-/lc) F-^pMpc
(9.45)
Jg
Jg
In the last two équations, which are now in standard form, ihe parallel axis
theorem was used, where
Jo — Jg +
(9.46)