一类具有球面叶层结构的二次广义Hamilton系统的分支结构
Bifurcation structure of a class of quadratic generalized Hamiltonian system with sphere leaves
摘要
具有球面叶层结构的二次广义Hamilton系统模型广泛存在于许多化学、物理、力学问题中.对此类系统的平衡点个数、稳定性随参数变化的规律进行了较深入的研究,获得了Hamilton函数H=21u2+21λv2+Au+Bv+Cw中λ=1时的全局相图.
A generalized Hamiltonian system with sphere leaves was studied, bifurcation and stability of equilibria were discussed in detail. The phase portraits with Hamilton function H=1/2U^2＋1/2λu^2＋Au＋Bu＋Cwwhen λ = 1 were obtained on sphere leaves.
出处
《浙江师范大学学报（自然科学版）》
CAS
2010年第3期266-270,共5页
Journal of Zhejiang Normal University:Natural Sciences
基金
国家自然科学基金资助项目(10872183)
参考文献9
-
1Arnold V I.Dynamical systems Ⅲ[M].Berlin:Springer-Verlag,1988.
-
2Arnold V I.Mathematical methods of classical mechanics[M].2nd ed.New York:Springer-Verlag,1989.
-
3Pyshchev A P.Classical approach to effective rotational energy and bifurcation in rotational dynamics of H2X molecules[J].Physical Review A,2003,68(4):1-10.
-
4Zhilinski B I.Symmetry invariants and topology in molecular models[J].Physics Reports,2001,341(1/2/3/4/5/6):85-171.
-
5Frauendiener J.Quadratic Hamiltonians on the unit sphere[J].Mech Res Commun,1995,22(4):313-317.
-
6Lanchares V,Elipe A.Bifurcations in biparametric quadratic potentials[J].Chaos,1995,5(2):367-373.
-
7Lanchares V,Elipe A.Bifurcations in biparametric quadratic potentials Ⅱ[J].Chaos,1995,5(3):531-535.
-
8Lanchares V,Inarrea M,Salas J P,et al.Surfaces of bifurcation in a triparametric quadratic Hamiltonian[J].Physical Review E,1995,52(5):5540-5548.
-
9Elipe A,Lanchares V.Exact solution of a triaxial gyrostat with one rotor[J].Celest Mech Dyn Astr,2008,101(1/2):49-68.
