Research output: Contribution to journal › Article › peer-review
Homogeneous Stäckel-type systems. / Tsyganov, A. V.
In: Theoretical and Mathematical Physics, Vol. 115, No. 1, 01.01.1998, p. 377-395.Research output: Contribution to journal › Article › peer-review
}
TY - JOUR
T1 - Homogeneous Stäckel-type systems
AU - Tsyganov, A. V.
PY - 1998/1/1
Y1 - 1998/1/1
N2 - A class of Hamiltonian dynamic systems integrated by the variable separation method is considered. The integration for this class is the inversion of an Abel mapping on hyperelliptic curves. We prove that the derivative of the Abel mapping is the Stäckel matrix, which determines a diagonal Riemannian metric and curvilinear orthogonal coordinate systems in a flat space. Lax representations with the spectral parameter are constructed. The corresponding classical r-matrices are dynamic. It is shown how the class of pointwise canonical transformations can be naturally generalized using the Abel integral reduction theory.
AB - A class of Hamiltonian dynamic systems integrated by the variable separation method is considered. The integration for this class is the inversion of an Abel mapping on hyperelliptic curves. We prove that the derivative of the Abel mapping is the Stäckel matrix, which determines a diagonal Riemannian metric and curvilinear orthogonal coordinate systems in a flat space. Lax representations with the spectral parameter are constructed. The corresponding classical r-matrices are dynamic. It is shown how the class of pointwise canonical transformations can be naturally generalized using the Abel integral reduction theory.
UR - http://www.scopus.com/inward/record.url?scp=0032355156&partnerID=8YFLogxK
U2 - 10.1007/BF02575497
DO - 10.1007/BF02575497
M3 - Article
AN - SCOPUS:0032355156
VL - 115
SP - 377
EP - 395
JO - Theoretical and Mathematical Physics (Russian Federation)
JF - Theoretical and Mathematical Physics (Russian Federation)
SN - 0040-5779
IS - 1
ER -
ID: 36285182