We use Lanczos equations to analyze the motion of shells in the gravitation
al field of a spherically symmetric central body. A first integral of Israe
l's matching conditions is used to show that the motion of the shell depend
s on the equation of state of the shell matter. In particular, the case of
a barotropic equation of state is analyzed. The question of how the type of
motion determines the equation of state for the matter of the shell is als
o investigated.