This article is cited in 5 papers

On the Regular Reduction of the n-Dimensional Problem of $N+1$ Bodies to Euler–Poincaré Equations on the Lie Algebra $sp(2N)$

S. T. Sadetov

Don State Technical University, Pl. Gagarina 1, 344010, Rostov-na-Donu, Russia

Abstract: After the lowering of the order up to the location of the center of inertia the reduction of this paper is performed by the passage to the complete set of invariants of the action of linear group of rotations and reflections on the phase space $\mathrm{T} ^* \mathbb{R}^n \otimes \mathbb{R}^N$. In distinction to known reductions, this reduction is homeomorphic. For $N+1=3$,$n=3,2$ the orbits of the coadjoint representation of the group $Sp(4)$, on which real motions take place, have the homotopy type of projective space $\mathbb{R} P^3$, sphere $S^2$, homogeneous space $(S^2 \times S^1) / \mathbb{Z}^2$.

MSC: 70F10, 34C20

Received: 20.05.2002

Language: English

DOI: 10.1070/RD2002v007n03ABEH000216

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