  The subject of this paper is the secular behaviour of a pair of planets
evolving under dissipative forces. In particular, we investigate the case when
dissipative forces affect the planetary semi-major axes and the planets move
inward/outward the central star, in a process known as planet migration. To
perform this investigation, we introduce fundamental concepts of conservative
and dissipative dynamics of the three-body problem. Based on these concepts, we
develop a qualitative model of the secular evolution of the migrating planetary
pair. Our approach is based on analysis of the energy and the orbital angular
momentum exchange between the two-planet system and an external medium; thus no
specific kind of dissipative forces is invoked. We show that, under assumption
that dissipation is weak and slow, the evolutionary routes of the migrating
planets are traced by the Mode I and Mode II stationary solutions of the
conservative secular problem. The ultimate convergence and the evolution of the
system along one of these secular modes of motion is determined uniquely by the
condition that the dissipation rate is sufficiently smaller than the proper
secular frequency of the system. We show that it is possible to reassemble the
starting configurations and migration history of the systems on the basis of
their final states and consequently to constrain the parameters of the physical
processes involved.
