On the stability problem and a bifurcation phenomenon for a special class of equilibria of the free rigid body on $\mathfrak{so}(5)$

Details On the stability problem and a bifurcation phenomenon for a special class of equilibria of the free rigid body on $\mathfrak{so}(5)$ On the stability problem and a bifurcation phenomenon for a special class of equilibria of the free rigid body on $\mathfrak{so}(5)$

2011-03-29

arxiv.org/abs/1103.5583v2

Mathematics

Dynamical Systems

This paper has been withdrawn by the author due to reorganization of the material and addition of some new remarks

Scientific paper

The stability of a special class of equilibria for the free rigid body on $\mathfrak{so}(5)$ is discussed. An instability region and two stability regions are established. The list of constants of motion which assure the complete integrability of the system is presented and used in the approach of stability with energy methods. The importance of appropriate choosing for the constants of motion in the energy methods is pointed out. A set of non-canonical constants of motion for the free rigid body on $\mathfrak{so}(5)$ and their role are analyzed.

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