  We generalize the Laplace resonance among three satellites, S1, S2 , and S3,
by considering different ratios of the mean-longitude variations. These
resonances, which we call Laplace-like, are classified as first order in the
cases of the 2:1&2:1, 3:2&3:2, and 2:1&3:2 resonances, second order in the case
of the 3:1&3:1 resonance, and mixed order in the case of the 2:1&3:1 resonance.
We consider a model that includes the gravitational interaction with the
central body together with the effect due to its oblateness, the mutual
gravitational influence of the satellites S1, S2, and S3 and the secular
gravitational effect of a fourth satellite S 4 , which plays the role of
Callisto in the Galilean system. In addition, we consider the dissipative
effect due to the tidal torque between the inner satellite and the central
body. We investigate these Laplace-like resonances by studying different
aspects: (i) we study the survival of the resonances when the dissipation is
included, taking two different expressions for the dissipative effect in the
case of a fast- or a slowly rotating central body, (ii) we investigate the
behavior of the Laplace-like resonances when some parameters are varied,
specifically, the oblateness coefficient, the semimajor axes, and the
eccentricities of the satellites, (iii) we analyze the linear stability of
first-order resonances for different values of the parameters, and (iv) we also
include the full gravitational interaction with S 4 to analyze its possible
capture into resonance. The results show a marked difference between first-,
second-, and mixed-order resonances, which might find applications when the
evolutionary history of the satellites in the Solar System are studied, and
also in possible actual configurations of extrasolar planetary systems.
