  The dynamic equation of mass point in rotating coordinates is governed by
Coriolis and centrifugal force, besides a corotating potential relative to
frame. Such a system is no longer a canonical Hamiltonian system so that the
construction of symplectic integrator is problematic. In this paper, we present
three integrators for this question. It is significant that those schemes have
the good property of near-conservation of energy. We proved that the discrete
symplectic map of $(p_n, x_n) \mapsto (p_{n+1}, x_{n+1})$ in corotating
coordinates exists and the two integrators are variational symplectic. Two
groups of numerical experiments demonstrates the precision and long-term
convergence of these integrators in the examples of corotating top-hat density
and circular restricted three-body system.

Instrumentation and Methods for Astrophysics