Necessary conditions for partial and super-integrability of Hamiltonian systems with homogeneous potentia
| dc.creator | Maciejewski, Andrzej J. | |
| dc.creator | Przybylska, Maria | |
| dc.creator | Yoshida, Haruo | |
| dc.date | 2007-01-29 | |
| dc.date.accessioned | 2026-07-07T07:43:40Z | |
| dc.date.available | 2026-07-07T07:43:40Z | |
| dc.description | We consider a natural Hamiltonian system of $n$ degrees of freedom with a homogeneous potential. Such system is called partially integrable if it admits $1<l<n$ independent and commuting first integrals, and it is called super-integrable if it admits $n+l$, $0<l<n$ independent first integrals such that $n$ of them commute. We formulate two theorems which give easily computable and effective necessary conditions for partial and super-integrability. These conditions are derived in the frame of the Morales-Ramis theory, i.e., from an analysis of the differential Galois group of variational equations along a particular solution of the system. To illustrate an application of the formulated theorems, we investigete three and four body problems on a line and the motion in a radial potential. | |
| dc.description | submitted to Nonlinearity | |
| dc.identifier | https://arxiv.org/abs/nlin/0701057 | |
| dc.identifier | http://arxiv.org/abs/nlin/0701057 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122914 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | Necessary conditions for partial and super-integrability of Hamiltonian systems with homogeneous potentia | |
| dc.type | text |