کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9501676 | 1338770 | 2005 | 8 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The influence of the kinetic energy in equilibrium of Hamiltonian systems
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
We provide a simple and explicit example of the influence of the kinetic energy in the stability of the equilibrium of classical Hamiltonian systems of the type H(q,p)=+Ï(q). We construct a potential energy Ï of class Ck with a critical point at 0 and two different positive defined matrices B1andB2, both independent of q, and show that the equilibrium (0,0) is stable according to Lyapunov for the Hamiltonian H1=+Ï(q), while for H2=+Ï(q) the equilibrium is unstable. Moreover, we give another example showing that even in the analytical situation the kinetic energy has influence in the stability, in the sense that there is an analytic potential energy Ï and two kinetic energies, also analytic, T1 and T2 such that the attractive basin of (0,0) is a two-dimensional manifold in the system of Hamiltonian Ï+T1 and a one-dimensional manifold in the system of Hamiltonian Ï+T2.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 213, Issue 2, 15 June 2005, Pages 410-417
Journal: Journal of Differential Equations - Volume 213, Issue 2, 15 June 2005, Pages 410-417
نویسندگان
M.V.P. Garcia, F.A. Tal,