On Periodic Solutions of One Second-Order Differential Equation

被引：0

作者：

Demidenko G.V. ^{[1
]}

Dulepova A.V. ^{[2
]}

机构：

[1] Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

[2] Novosibirsk State University, Novosibirsk

来源：

Journal of Mathematical Sciences | 2024年 / 278卷 / 2期

关键词：

asymptotical stability; inverted pendulum; periodic solution; second-order differential equation;

D O I：

10.1007/s10958-024-06922-7

中图分类号：

学科分类号：

摘要：

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. © 2024, Springer Nature Switzerland AG.

引用

页码：314 / 327

页数：13

共 50 条

[21] Positive periodic solutions of second-order differential equations
Wang, Weibing
Luo, Zhiguo
[J]. APPLIED MATHEMATICS LETTERS, 2007, 20 (03) : 266 - 271
[22] Periodic solutions of the second-order differential equations with singularity
Wang, ZH
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2004, 58 (3-4) : 319 - 331
[23] Periodic Solutions of a Second-Order Functional Differential Equation with State-Dependent Argument
Zhao, Hou Yu
Liu, Jia
[J]. MEDITERRANEAN JOURNAL OF MATHEMATICS, 2018, 15 (06)
[24] ON PERIODIC SOLUTIONS OF SEVERAL CLASSES OF RICCATI’S EQUATION AND SECOND-ORDER DIFFERENTIAL EQUATIONS
李鸿祥
[J]. Applied Mathematics and Mechanics(English Edition), 1982, (02) : 225 - 232
[25] Positive solutions of periodic boundary value problems for the second-order differential equation with a parameter
Ying Wang
Jing Li
Zengxia Cai
[J]. Boundary Value Problems, 2017
[26] Positive solutions of periodic boundary value problems for the second-order differential equation with a parameter
Wang, Ying
Li, Jing
Cai, Zengxia
[J]. BOUNDARY VALUE PROBLEMS, 2017,
[27] A Remark on the Theory of Periodic Solutions of a Lyapunov Type Second-Order Matrix Differential Equation
V. N. Laptinskii
V. A. Livinskaya
[J]. Differential Equations, 2002, 38 : 1211 - 1212
[28] Periodic Solutions of a Second-Order Functional Differential Equation with State-Dependent Argument
Hou Yu Zhao
Jia Liu
[J]. Mediterranean Journal of Mathematics, 2018, 15
[29] Existence of periodic solutions for a class of second-order differential equation with multiple deviating arguments
Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China
不详
[J]. Zhongshan Daxue Xuebao, 2007, 6 (5-9): : 5 - 9
[30] PERIODIC SOLUTIONS OF A NONLINEAR SECOND ORDER DIFFERENTIAL EQUATION
UTZ, WR
[J]. SIAM JOURNAL ON APPLIED MATHEMATICS, 1970, 19 (01) : 56 - &

← 1 2 3 4 5 →