2015/04/30 by Davit R. Petrosyan, D. R. Petrosyan, G. S. Pogosyan +2 · 3 citations
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Bounded function #Classical mechanics #Constant (computer programming) #Constant curvature #Curvature #Equidistant #Geometry #Harmonic oscillator #Hyperboloid #Mathematical analysis #Mathematical physics #Mathematics #Motion (physics) #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #math-ph #math.MP #msc:35F21 #msc:70H20
paper · pdf · doi:10.3842/sigma.2015.096
published in Symmetry Integrability and Geometry Methods and Applications (National Academy of Sciences of Ukraine)
arxiv created 2015/11/25 · openalex publication_date 2015/11/25 · arxiv updated 2015/11/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In the present work the classical problem of harmonic oscillator in the hyperbolic space H 2 2 : z 2 0 +z 2 1 -z 2 2 -z 2 3 = R 2 has been completely solved in framework of Hamilton-Jacobi equation. We have shown that the harmonic oscillator on H 2 2 , as in the other spaces with constant curvature, is exactly solvable and belongs to the class of maximally superintegrable system. We have proved that all the bounded classical trajectories are closed and periodic. The orbits of motion are ellipses or circles for bounded motion and ultraellipses or equidistant curve for infinite ones.