Analytical expressions for stability regions in the Ince-Strutt diagram of Mathieu equation

Simple analytical expressions are suggested for transition curves that separate, in the Ince-Strutt diagram, different types of solutions to the famous Mathieu equation. The derivations of these expressions in this paper rely on physically meaningful periodic solutions describing various regular motions of a familiar nonlinear mechanical system-a rigid planar pendulum with a vertically oscillating pivot. The paper is accompanied by a relevant simulation program. (C) 2018 American Association of Physics Teachers.