TY - JOUR

T1 - On Periodic Solutions of One Second-Order Differential Equation

AU - Demidenko, G. V.

AU - Dulepova, A. V.

PY - 2024/1

Y1 - 2024/1

N2 - In this paper, we investigate the motion of an inverted pendulum, the suspension point of which performs high-frequency oscillations along a line making a small angle with the vertical. We prove that under certain conditions on the function describing the oscillations of the suspension point of the pendulum, a periodic motion of the pendulum arises, and it is asymptotically stable.

AB - In this paper, we investigate the motion of an inverted pendulum, the suspension point of which performs high-frequency oscillations along a line making a small angle with the vertical. We prove that under certain conditions on the function describing the oscillations of the suspension point of the pendulum, a periodic motion of the pendulum arises, and it is asymptotically stable.

KW - asymptotical stability

KW - inverted pendulum

KW - periodic solution

KW - second-order differential equation

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85182487980&origin=inward&txGid=fc424bcb85e2aaf3ee8c8e2f545c89f8

UR - https://www.mendeley.com/catalogue/d93fd26f-e9e8-350e-80e8-ae60f6ab7dc6/

U2 - 10.1007/s10958-024-06922-7

DO - 10.1007/s10958-024-06922-7

M3 - Article

VL - 278

SP - 314

EP - 327

JO - Journal of Mathematical Sciences (United States)

JF - Journal of Mathematical Sciences (United States)

SN - 1072-3374

IS - 2

ER -