含有约束的两个状态变量系统的转迁集计算

李军; 陈予恕

doi:10.3879/j.issn.1000-0887.2012.02.001

含有约束的两个状态变量系统的转迁集计算

doi: 10.3879/j.issn.1000-0887.2012.02.001

李军,
陈予恕

哈尔滨工业大学航天学院137信箱,哈尔滨 150001

基金项目: 国家自然科学基金资助项目（10632040）

详细信息

通讯作者:
李军(1982—),男,河北沧州人,博士生(联系人.Tel:+86-451-82151191;E-mail:y8a82000@163.com).

中图分类号: O322;TH133
计量
- 文章访问数: 1694
- HTML全文浏览量: 106
- PDF下载量: 783
- 被引次数: 0
出版历程
- 收稿日期: 2011-08-19
- 修回日期: 2011-12-04
- 刊出日期: 2012-02-15

Transition Sets of Bifurcations of Dynamical System With Two State Variables With Constraints

LI Jun,
CHEN Yu-shu

School of Astronautics, Harbin Institute of Technology, P.O.Box 137, Harbin 150001, P.R.China

摘要

摘要: 周期解的分岔广泛存在于实际的非线性动力学系统中．该文对两个状态变量系统的约束分岔进行了讨论．在约束条件下系统将产生新的转迁集．此外，以一个二维系统为例，对含有约束条件和不含有约束条件的分岔特性进行了比较．所得的结果可以为系统的设计和参数选择提供理论依据．
- 分岔 /
- 约束 /
- 奇异性理论 /
- 非线性动力学 /
- 两状态变量
Abstract: Bifurcation of periodic solutions widely exists in nonlinear dynamical systems. Categories of bifurcations of systems with two state variables with different types of constraints were discussed where some new types of transition sets were added. Additionally, the bifurcation properties of two-dimensional systems without constraints were compared with the ones with constraints. The results obtained can be used by engineers for the choice of the structural parameters of the system.
- bifurcation /
- constraint /
- singularity theory /
- nonlinear dynamics /
- two state variables

HTML全文

参考文献(11)

[1]	Chen Y S, Langford W F. The subharmonic bifurcation solution of nonlinear Mathieu’s equation and Euler dynamically buckling problems[J]. Acta Mechanica Sinica, 1988, 20(6): 522-632.
[2]	陈予恕, 丁千. C-L方法及其在工程非线性动力学问题中的应用[J]. 应用数学和力学, 2001, 22(2): 127-134.(CHEN Yu-shu, DING Qian. C-L method and its application to engineering nonlinear dynamical problems[J]. Applied Mathematics and Mechanics(English Edition), 2001, 22(2): 144-153.)
[3]	Chen Y S, Xu J. Universal classification of bifurcating solutions to a primary parametric resonance in van der Pol-Duffing-Mathicu’s systems[J].J Science in China, 1996, 39(4): 405-417.
[4]	吴志强, 陈予恕. 具有单边约束的基本分岔问题的新分岔模式[J]. 应用数学和力学, 2001, 22(11): 1135-1141.(WU Zhi-qing, CHEN Yu-shu. New bifurcation patterns in elementary bifurcation problems with single-side constraint[J]. Applied Mathematics and Mechanics(English Edition), 2001, 22(11): 1260-1267.)
[5]	吴志强, 陈予恕. 含约束非线性动力系统的分岔分类[J]. 应用数学和力学, 2002, 23(5): 477-482.(WU Zhi-qing, CHEN Yu-shu. Classification of bifurcations for nonlinear dynamical problems with constraints[J]. Applied Mathematics and Mechanics(English Edition), 2002, 23(5): 535-541.)
[6]	Wu Z Q, Yu P, Wang K Q. Bifurcation analysis on a self-excited hysteretic system[J]. International Journal of Bifurcation and Chaos, 2004, 14(8): 2825-2842.
[7]	吴志强, 丁然, 陈予恕. 约束含参分岔问题的分类[J]. 应用数学和力学, 2010, 31(2): 127-133.(WU Zhi-qing, DING Ran, CHEN Yu-shu. Classification of parametrically constrained bifurcations[J]. Applied Mathematics and Mechanics(English Edition), 2010, 31(2): 135-142.)
[8]	胡凡努, 李养成. 关于两个状态变量组的等变分歧问题的通用开折[J]. 数学理论与应用, 2000, 20(3): 50-57.(HU Fan-nu, LI Yang-cheng. Versal unfolding of equivariant bifurcation problems with two types of state variables[J]. Mathematical Theory and Application, 2000, 20(3): 50-57.（in Chinese）)
[9]	秦朝红, 陈予恕, 李军. 1∶1内振悬索的二维奇异性分析[J]. 应用数学和力学, 2010, 31(2): 134-142.(QIN Zhao-hong, CHEN Yu-shu, LI Jun. singularity analysis of a two-dimensional elastic cable with 1∶1 internal resonance[J]. Applied Mathematics and Mechanics(English Edition), 2010, 31(2): 143-150.)
[10]	Golubitsky M, Schaeffer D G. Singularities and Groups in Bifurcation Theory[M]. NY: Spring-Verlag, 1985.
[11]	Chen Y S, Qin Z H. Singular analysis of two-dimensional bifurcation system[J].Science China Technological Sciences, 2010, 53(3): 608-611.