TY - JOUR

T1 - Analytical expressions for stability regions in the Ince-Strutt diagram of Mathieu equation

AU - Butikov, Eugene I.

PY - 2018/4/1

Y1 - 2018/4/1

N2 - 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.

AB - 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.

KW - INVERTED PENDULUM

UR - http://www.scopus.com/inward/record.url?scp=85044330630&partnerID=8YFLogxK

U2 - 10.1119/1.5021895

DO - 10.1119/1.5021895

M3 - Article

AN - SCOPUS:85044330630

VL - 86

SP - 257

EP - 267

JO - American Journal of Physics

JF - American Journal of Physics

SN - 0002-9505

IS - 4

ER -