arXiv subjects

H. Gümral

Publications and source records attributed to H. Gümral.

2 recordsLinked to original sources

arXiv2023

Oscillator Algebra of Chiral Oscillator

For the chiral oscillator described by a second order and degenerate Lagrangian with special Euclidean group of symmetries, we show, by cotangent bundle Hamiltonian reduction, that reduced equations are Lie-Poisson on dual of oscillator algebra, the central extension of special Euclidean algebra in two dimensions. This extension, defined by symplectic two-cocycle of special Euclidean algebra, seems to be an enforcement of reduction itself rooted to Casimir function.

math-ph↗

arXiv2011

Poisson Structures for Aristotelian Model of Three Body Motion

We present explicitly Poisson structures, for both time-dependent and time-independent Hamiltonians, of a dynamical system with three degrees of freedom introduced and studied by Calogero et al [2005]. For the time-independent case, new constant of motion includes all parameters of the system. This extends the result of Calogero et al [2009] for semi-symmetrical motion. We also discuss the case of three bodies two of which are not interacting with each other but are coupled with the interaction of third one.

math-ph↗