Stability sets of multiparameter Hamiltonian systems

被引:17
作者
Batkhin, A. B.
Bruno, A. D.
Varin, V. P.
机构
来源
PMM JOURNAL OF APPLIED MATHEMATICS AND MECHANICS | 2012年 / 76卷 / 01期
基金
俄罗斯基础研究基金会;
关键词
D O I
10.1016/j.jappmathmech.2012.03.006
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
A real linear Hamiltonian system with constant coefficients that depend on several real parameters is considered. A method is proposed for calculating the sets of all values of the parameters for which the stationary solution of this system is stable for fixed values of the parameters (that is, the stability sets). The application of the method is demonstrated for a gyroscopic problem described by a Hamiltonian system with four degrees of freedom and three parameters. Computer algebra, in particular, a Grobner basis and a Power Geometry are used. It is shown that the four-parameter generalization of this problem does not contain fundamentally new difficulties. (C) 2012 Elsevier Ltd. All rights reserved.
引用
收藏
页码:56 / 92
页数:37
相关论文
共 28 条
[1]  
[Anonymous], 1952, Theory of Stability of Motion
[2]  
[Anonymous], 1959, The Theory of Matrices
[3]  
Barnyak MYa, 1988, IZV AKAD NAUK SSSR M, V4, P51
[4]  
Batkhin AB, 2011, INT C POL ALG 2011, P17
[5]  
Batkhin AB, 2011, VESTNIK NIZHEGORODSK, V4, P57
[6]  
Batkhin AV, 2011, 42 MV KELD I PRIKL M
[7]   Asymptotic Solution of an Algebraic Equation [J].
Bruno, A. D. ;
Batkhin, A. B. .
DOKLADY MATHEMATICS, 2011, 84 (02) :634-639
[8]  
Bruno A.D., 2011, INT C POL ALG 2011, P25
[9]  
Bruno A.D., 2000, Power Geometry in Algebraic and Differential Equations
[10]  
Bruno A. D., 1994, RESTRICTED 3 BODY PR