This article is cited in 1 scientific paper (total in 1 paper)
Algebraic reduction of systems on two- and three-dimensional spheres
A. V. Borisov, I. S. Mamaev, S. M. Ramodanov
The paper develops further the algebraic-reduction method for $SO(4)$-symmetrie systems on the three-dimensional sphere. Canonical variables for the reduced system are constructed both on two-dimensional and three-dimensional spheres. The method is illustrated by applying it to the two-body problem on a sphere (the bodies are assumed to interact with a potential that depends only on the geodesic distance between them) and the three-vortex problem on a two-dimensional sphere.
Poisson structure. Lie algebra, subalgebra, Andoyer variables.
PDF file (180 kB)
MSC: 70Hxx, 70G65
A. V. Borisov, I. S. Mamaev, S. M. Ramodanov, “Algebraic reduction of systems on two- and three-dimensional spheres”, Nelin. Dinam., 4:4 (2008), 407–416
Citation in format AMSBIB
\by A.~V.~Borisov, I.~S.~Mamaev, S.~M.~Ramodanov
\paper Algebraic reduction of systems on two- and three-dimensional spheres
\jour Nelin. Dinam.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
A. A. Burov, “On the motion of a solid body on spherical surfaces”, Journal of Mathematical Sciences, 199:5 (2014), 501–509
|Number of views:|