Abstract
We introduce specific type of hyperbolic spaces. It is not a general linear covariant object, but is of use in constructing nilpotent systems. In the present work necessary definitions and relevant properties of configuration and phase spaces are indicated. As a working example we use aD=2 isotropic harmonic oscillator.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Frydryszak: Czech. J. Phys.55 (2005) 1409.
R. Berndt:An Introduction to Symplectic Geometry, Graduate Studies in Mathematics, Vol. 26, AMS, Providence, Rhode Island, 2001.
G.F. Torres del Castillo and M.P. Velázquez Quevada: Rev. Mex. Fis.50 (2006) 608.
A.A. Martínez-Merino and M. Montesinos: gr-qc/0601140.
J.F. Cariñena, M.F. Rañada, M. Santander, and T. Sanz-Gil: J. Nonlin. Math. Phys.12 (2005) 230.
J.M. Jauch and E.L. Hill: Phys. Rev.57 (1940) 641.
D.M. Fradkin: Am. J. Phys.33 (1965) 207.
Author information
Authors and Affiliations
Additional information
This work is supported by Polish KBN grant #1PO3B01828
Rights and permissions
About this article
Cite this article
Frydryszak, A.M. Nilpotent classical mechanics:s-geometry. Czech J Phys 56, 1155–1160 (2006). https://doi.org/10.1007/s10582-006-0417-7
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10582-006-0417-7