On the regular reduction of the \(n\)-dimensional problem of \(N+1\) bodies to Euler-Poincaré equations on the Lie algebra \(sp(2N)\)
The title reduction 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 \(T^\ast {\mathbb{R}}^n\otimes {\mathbb{R}}^N\). In contrast to known reductions, the reduction proposed is homeomorphic. For \(N+1=3\), \(n=3,2\), the orbits of the coadjoint representation of group \(Sp(4)\) on which real motions take place, have the homotopy type of the projective space \({\mathbb{R}}P^3\), the sphere \(S^3\), and the homogeneous space \((S^2 \times S^1)/{\mathbb{Z}}_2\).
scientific article; zbMATH DE number 1873412