On the symmetry of Hamiltonian systems
Küçük Resim Yok
Tarih
2009
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Maltepe Üniversitesi
Erişim Hakkı
CC0 1.0 Universal
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
Özet
In this paper, we use the formalism of Hamiltonian system on symplectic manifold due to Reeb[2] given in Abraham and Marsden[6] and Arnold[7] to derive the equation of motion for (1) A particle on a line in a plane with a spring force and (2) A free particle in n-space. The time flows for both the problems mentioned above are also determined and proved that the determined flow is a Hamiltonian flow, i.e., the symmetry of a Hamiltonian system. A non-Hamiltonian flow is also considered and it is shown that by changing the symplectic form and the phase space of the system we can convert it into a Hamiltonian flow. The translation and rotational symmetry related to linear and angular momentum respectively for the motion of a free particle in n-space is also considered, which is useful in reducing the phase space of a mechanical system.
Açıklama
Anahtar Kelimeler
Hamiltonian system, Symplectic manifold, Lie-group action, Hamiltonian flow
Kaynak
International Conference of Mathematical Sciences
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
Gupta, V. G. ve Sharma, P. (2009). On the symmetry of Hamiltonian systems. Maltepe Üniversitesi. s. 376.
