
Setting
_
p equal to zero in Equation 3.208 gives
x
3
(0) ¼ gx
1
(0)(3:209)
Initial depth x
1
(0) is arbitrary; however, to be in equilibrium, the diver’s effective weight in the
water W gV must be counterbalanced by the initial cable force f
c
(0).
f
c
(0) ¼ W gV (3:210)
Note that the initial net force to maintain the diver in equilibrium is
f
n
(0) ¼ (W gV) f
c
(0) ¼ 0 (3:211)
A simulation of the diver’s ascent subject to a constant cable force in excess of f
c
(0) in Equation
(3.210) is needed. The discrete-time state equation is
x
A
(n þ 1) ¼ Gx
A
(n) þ Hu(n)(3:212)
where G and H depend on the choice of numerical integrator. Using trapezoidal integration for now ...