Geometry of Hamiltonian Dynamics with Conformal Eisenhart Metric
Joint Authors
Sun, Huafei
Sun, Xiao
Peng, Linyu
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-26, 26 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-06-19
Country of Publication
Egypt
No. of Pages
26
Main Subjects
Abstract EN
We characterize the geometry of the Hamiltonian dynamics with a conformal metric.
After investigating the Eisenhart metric, we study the corresponding conformal metric and obtain the geometric structure of the classical Hamiltonian dynamics.
Furthermore, the equations for the conformal geodesics, for the Jacobi field along the geodesics, and the equations for a certain flow constrained in a family of conformal equivalent nondegenerate metrics are obtained.
At last the conformal curvatures, the geodesic equations, the Jacobi equations, and the equations for the flow of the famous models, an N degrees of freedom linear Hamiltonian system and the Hénon-Heiles model are given, and in a special case, numerical solutions of the conformal geodesics, the generalized momenta, and the Jacobi field along the geodesics of the Hénon-Heiles model are obtained.
And the numerical results for the Hénon-Heiles model show us the instability of the associated geodesic spreads.
American Psychological Association (APA)
Peng, Linyu& Sun, Huafei& Sun, Xiao. 2011. Geometry of Hamiltonian Dynamics with Conformal Eisenhart Metric. International Journal of Mathematics and Mathematical Sciences،Vol. 2011, no. 2011, pp.1-26.
https://search.emarefa.net/detail/BIM-492416
Modern Language Association (MLA)
Peng, Linyu…[et al.]. Geometry of Hamiltonian Dynamics with Conformal Eisenhart Metric. International Journal of Mathematics and Mathematical Sciences No. 2011 (2011), pp.1-26.
https://search.emarefa.net/detail/BIM-492416
American Medical Association (AMA)
Peng, Linyu& Sun, Huafei& Sun, Xiao. Geometry of Hamiltonian Dynamics with Conformal Eisenhart Metric. International Journal of Mathematics and Mathematical Sciences. 2011. Vol. 2011, no. 2011, pp.1-26.
https://search.emarefa.net/detail/BIM-492416
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-492416