Наукова електронна бібліотека
періодичних видань НАН України
періодичних видань НАН України
Harmonic Oscillator on the SO(2,2) Hyperboloid
Репозиторій DSpace/Manakin
- Домашня сторінка
- →
- Фізико-технічні та математичні науки
- →
- Відділення математики
- →
- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
- →
- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
- →
- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11, випуск за цей рік
- →
- Переглянути статтю
JavaScript is disabled for your browser. Some features of this site may not work without it.
Harmonic Oscillator on the SO(2,2) Hyperboloid
Інший ID:
2010 Mathematics Subject Classification: 22E60; 37J15; 37J50; 70H20
DOI:10.3842/SIGMA.2015.096
DOI:10.3842/SIGMA.2015.096
Посилання:
Harmonic Oscillator on the SO(2,2) Hyperboloid / D.R. Petrosyan, G.S. Pogosyan // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 51 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Analytical Mechanics and Dif ferential Geometry in honour
of Sergio Benenti. The full collection is available at http://www.emis.de/journals/SIGMA/Benenti.html.
The work of G.P. was partially supported under the Armenian-Belarus grant Nr. 13RB-035 and
Armenian national grant Nr. 13-1C288.
Дата:
2015
Переглядів:
557
Завантажень:
286
Анотація:
In the present work the classical problem of harmonic oscillator in the hyperbolic space H²₂: z²₀+z²₁−z²₂−z²₃=R² has been completely solved in framework of Hamilton-Jacobi equation. We have shown that the harmonic oscillator on H²₂, 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.
