Open Access

Poisson and symplectic reductions of 4–DOF isotropic oscillators. The van der Waals system as benchmark

F. Crespo

F. Crespo

Departamento de Matemática, Facultad de Ciencias, Universidad del Bío-BíoConcepción, Chile
Search for this author on
Sciendo|Google Scholar
Crespo, F.
, 
G. Díaz-Toca

G. Díaz-Toca

Departamento de Ingeniería y Tecnología de Computadores, Universidad de MurciaMurcia, Spain
Search for this author on
Sciendo|Google Scholar
Díaz-Toca, G.
, 
S. Ferrer

S. Ferrer

Departamento de Ingeniería y Tecnología de Computadores, Universidad de MurciaMurcia, Spain
Search for this author on
Sciendo|Google Scholar
Ferrer, S.
 and 
M. Lara

M. Lara

Space Dynamics Group, Polytechnic University of Madrid –UPMMadrid, Spain
Search for this author on
Sciendo|Google Scholar
Lara, M.
  
Oct 13, 2016
Poisson and symplectic reductions of 4–DOF isotropic oscillators. The van der Waals system as benchmark's Cover Image
About this article
Previous Article
Next Article
Cite
Download Cover
Published Online: Oct 13, 2016
Page range: 473 - 492
Received: Mar 12, 2016
Accepted: Oct 10, 2016
DOI: https://doi.org/10.21042/AMNS.2016.2.00038
Keywords
© 2016 F. Crespo, G. Díaz–Toca, S. Ferrer, M. Lara, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Double reduced spaces Sn+ξ2×Sn−ξ2$\begin{array}{} \displaystyle S_{n + \xi }^2 \times S_{n - \xi }^2 \end{array}$ for different values of the integral ξ
Double reduced spaces Sn+ξ2×Sn−ξ2$\begin{array}{} \displaystyle S_{n + \xi }^2 \times S_{n - \xi }^2 \end{array}$ for different values of the integral ξ

Fig. 2

Thrice reduced space over the space of integrals. The vector (K, N, S) represents the coordinates. The axis of symmetry of the reduced space is the K direction.
Thrice reduced space over the space of integrals. The vector (K, N, S) represents the coordinates. The axis of symmetry of the reduced space is the K direction.

Poisson structure in (M, N, Z, S, K, L1) invariants

{,}MNZSKL1
M04KS0−4KN00
N−4KS0−4L1S−4(KM – L1Z)4S0
Z04L1S0−4L1N00
S4KN4(KM – L1Z)4L1N0−4N0
K0−4S04N00
L1000000
Language:
English
Publication timeframe:
1 times per year
Journal Subjects:
Life Sciences, Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics, Physics, other
Journal RSS Feed