The parametric instability of resonance motion in restricted three body problem

A method of analyses of dynamical system is applied to the planetary restricted three-body problem (RTBP). It is well known, that equations of motion of restricted 3-body problem in rotating rectangular frame may be reduced to the second order differential equation with periodic coefficients (Hills equation). Here Hills equation in cylindrical coordinate frame is derived. It gives the possibility to estimate width and position of the unstable zones. The dependence of the position of unstable zones on orbital eccentricity of the test particle is derived. Some followings of this simple linear model are noted.