  For a mechanical system consisting of a rotator and a pendulum coupled via a
small, time-periodic Hamiltonian perturbation, the Arnold diffusion problem
asserts the existence of `diffusing orbits' along which the energy of the
rotator grows by an amount independent of the size of the coupling parameter,
for all sufficiently small values of the coupling parameter. There is a vast
literature on establishing Arnold diffusion for such systems. In this work, we
consider the case when an additional, dissipative perturbation is added to the
rotator-pendulum system with coupling. Therefore, the system obtained is not
symplectic but conformally symplectic. We provide explicit conditions on the
dissipation parameter, so that the resulting system still exhibits energy
growth. The fact that Arnold diffusion may play a role in systems with small
dissipation was conjectured by Chirikov. In this work, the coupling is
carefully chosen, however the mechanism we present can be adapted to general
couplings and we will deal with the general case in future work.
