The symmetry of steady-state solutions of non-smooth dynamical systems with two constraints

被引：2
|
作者：
Luo, ACJ [1 ]
机构：
[1] So Illinois Univ, Dept Mech & Ind Engn, Edwardsville, IL 62026 USA
来源：
PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART K-JOURNAL OF MULTI-BODY DYNAMICS | 2005年 / 219卷 / 01期
关键词：
non-smooth dynamical systems; mapping dynamics; local singularity; symmetry invariance;
D O I：
10.1243/146441905X9980
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
In this paper, the symmetry of steady-state solutions in non-smooth dynamical systems with two symmetrical constraints are investigated to obtain all possible stable and unstable motions. An invariant transformation exists in regular and chaotic motions relative to skew-symmetrical mapping pairs in symmetrical systems with harmonic excitations. This investigation provides a mathematical foundation for the symmetry of solutions in this class of non-smooth dynamical systems. The group structure of mapping combinations should be further investigated.
引用
收藏
页码：109 / 124
页数：16
相关论文
共 50 条
  • [21] On Constraints in First-Order Optimization: A View from Non-Smooth Dynamical Systems
    Muehlebach, Michael
    Jordan, Michael I.
    [J]. Journal of Machine Learning Research, 2022, 23
  • [22] On the birth of limit cycles for non-smooth dynamical systems
    Llibre, Jaume
    Novaes, Douglas D.
    Teixeira, Marco A.
    [J]. BULLETIN DES SCIENCES MATHEMATIQUES, 2015, 139 (03): : 229 - 244
  • [23] Computation of the Basins of Attraction in Non-smooth Dynamical Systems
    Galvanetto, Ugo
    Colombo, Alessandro
    [J]. IUTAM SYMPOSIUM ON NONLINEAR DYNAMICS FOR ADVANCED TECHNOLOGIES AND ENGINEERING DESIGN, 2013, 32 : 17 - 29
  • [24] Hopf Bifurcation for Non-smooth Planar Dynamical Systems
    邹永魁
    Tassilo Küpper
    [J]. Communications in Mathematical Research, 2001, (03) : 261 - 264
  • [25] Some Non-smooth Dynamical Systems in Offshore Mechanics
    Virgin, L. N.
    Plaut, R. H.
    [J]. VIBRO-IMPACT DYNAMICS OF OCEAN SYSTEMS AND RELATED PROBLEMS, 2009, 44 : 259 - +
  • [26] A very non-smooth maximum principle with state constraints
    Sussmann, Hector J.
    [J]. 2005 44th IEEE Conference on Decision and Control & European Control Conference, Vols 1-8, 2005, : 917 - 922
  • [27] Steady-state responses of mechanical system attached to non-smooth vibration absorber with piecewise damping and stiffness
    Sun, Min
    Hu, Wen-hua
    Liu, Jun
    Chen, Jian-en
    [J]. MECCANICA, 2021, 56 (02) : 275 - 285
  • [28] Steady-state responses of mechanical system attached to non-smooth vibration absorber with piecewise damping and stiffness
    Min Sun
    Wen-hua Hu
    Jun Liu
    Jian-en Chen
    [J]. Meccanica, 2021, 56 : 275 - 285
  • [29] Non-constant steady-state solutions for Brusselator type systems
    Ghergu, Marius
    [J]. NONLINEARITY, 2008, 21 (10) : 2331 - 2345
  • [30] Extreme Value Laws in Dynamical Systems for Non-smooth Observations
    Ana Cristina Moreira Freitas
    Jorge Milhazes Freitas
    Mike Todd
    [J]. Journal of Statistical Physics, 2011, 142 : 108 - 126
12345