Physics – Mathematical Physics
Scientific paper
2008-03-03
J. Phys. A: Math. Gen., vol. 41, issue 37, (2008)
Physics
Mathematical Physics
17 pages, 1 figure
Scientific paper
10.1088/1751-8113/41/39/395201
In this paper we study the Neumann system, which describes the harmonic oscillator (of arbitrary dimension) constrained to the sphere. In particular we will consider the confluent case where two eigenvalues of the potential coincide, which implies that the system has S^{1} symmetry. We will prove complete algebraic integrability of confluent Neumann system and show that its flow can be linearized on the generalized Jacobian torus of some singular algebraic curve. The symplectic reduction of S^{1} action will be described and we will show that the general Rosochatius system is a symplectic quotient of the confluent Neumann system, where all the eigenvalues of the potential are double. This will give a new mechanical interpretation of the Rosochatius system.
No associations
LandOfFree
Algebraic integrability of confluent Neumann system does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Algebraic integrability of confluent Neumann system, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Algebraic integrability of confluent Neumann system will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-225374