Integrable systems, Lax representations, and confocal quadrics. (English) Zbl 0841.35112
Kozlov, V. V. (ed.), Dynamical systems in classical mechanics. Transl., Ser. 2, Am. Math. Soc. 168(25), 173-199 (1995).
The equations of free motion of an \(m\)-dimensional rigid body have the form
\[
\mathring M= [M, \Omega],\quad \Omega= {\partial H\over \partial M},\tag{1}
\]
where \(\Omega\in \text{SO}(m)\), \(M\in \text{SO}^*(m)\). The paper displays a close connection between families of confocal quadrics and \(m\)-dimensional integrable Hamiltonian systems (1).
For the entire collection see [Zbl 0827.00018].
For the entire collection see [Zbl 0827.00018].
Reviewer: L.A.Sakhnovich (Odessa)
MSC:
| 35Q58 | Other completely integrable PDE (MSC2000) |
| 37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 70E15 | Free motion of a rigid body |
