  We develop here the method for obtaining approximate stability boundaries in
the space of parameters for systems with parametric excitation. The monodromy
(Floquet) matrix of linearized system is found by averaging method. For system
with 2 degrees of freedom (DOF) we derive general approximate stability
conditions. We study domains of stability with the use of fourth order
approximations of monodromy matrix on example of inverted position of a
pendulum with vertically oscillating pivot. Addition of small damping shifts
the stability boundaries upwards, thus resulting to both stabilization and
destabilization effects.
