TY - JOUR

T1 - On Stability of the Inverted Pendulum Motion with a Vibrating Suspension Point

AU - Demidenko, G. V.

AU - Dulepova, A. V.

N1 - Publisher Copyright: © 2018, Pleiades Publishing, Ltd.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - Under study is the stability of the inverted pendulum motion whose suspension point vibrates according to a sinusoidal law along a straight line having a small angle with the vertical. Formulating and using the contracting mapping principle and the criterion of asymptotic stability in terms of solvability of a special boundary value problem for the Lyapunov differential equation, we prove that the pendulum performs stable periodic movements under sufficiently small amplitude of oscillations of the suspension point and sufficiently high frequency of oscillations.

AB - Under study is the stability of the inverted pendulum motion whose suspension point vibrates according to a sinusoidal law along a straight line having a small angle with the vertical. Formulating and using the contracting mapping principle and the criterion of asymptotic stability in terms of solvability of a special boundary value problem for the Lyapunov differential equation, we prove that the pendulum performs stable periodic movements under sufficiently small amplitude of oscillations of the suspension point and sufficiently high frequency of oscillations.

KW - asymptotic stability

KW - contracting mapping principle

KW - inverted pendulum

KW - Lyapunov differential equation

UR - http://www.scopus.com/inward/record.url?scp=85058104576&partnerID=8YFLogxK

U2 - 10.1134/S1990478918040026

DO - 10.1134/S1990478918040026

M3 - Article

AN - SCOPUS:85058104576

VL - 12

SP - 607

EP - 618

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 4

ER -