SPINAL INJURY CONTROL - Injury Biomechanics and Control: Optimal Protection from Impact - page 194

the configuration of the dummy and its position relative to the seat pan.
Therefore,

ξ dc = ξ dc (q). (5.86)

Using the time history of the absolute acceleration of the seat pan, u s (t) ,
as the input for the MADYMO simulation of the dummy response, one
can calculate the time histories of the generalized coordinates q(t) and the
appropriate response characteristics of the occupant model and, in particu-
lar, the maximum magnitude of the spinal compressive force J 2 (u s ) ,where
J 2 (u s ) is used to denote the maximum magnitude of the spinal compres-
sive force to be consistent with the notation of Problems 5.1 - 5.4. This
calculation is based on the numerical solution of the equations of motion
of the dummy. These equations of motion are generated and integrated
automatically by MADYMO and are not accessible to the user. Of course,
it is necessary to specify initial conditions of the coordinates q and their
derivatives q : ˙

q( 0 ) = q 0 , q( 0 ) = q 0 . (5.87)

Assume that at the initial time instant t = 0 the dummy does not move

relative to the seat pan and, accordingly, 0. The initial configuration

of the seated dummy corresponds to equilibrium from the influence of
the forces acting between the dummy components, the forces due to the
interaction of the dummy with the seat, and gravity. The initial configuration
isshowninFig.5.9.
The shock pulse applied to the airframe is modeled by the half-sine wave
of Eq. (5.10).

q 0 ˙ =

FIGURE 5.9 Initial configuration of the MADYMO model of the occupant.