Colloquium

Colloquium
Linear Stability for a Certain Class of Equilibria of an $SO(n)$ Free Rigid Body Tarama Daisuke 16th July (Fri) 13:30 In this talk, studied is the stability of a certain class of equilibria of an $SO(n)$ free rigid body. The coordinate type Cartan subalgebra in $\mathfrak{so}(n)$ is defined and its characterization is obtained in relation with the Manakov integrals. The stability analysis is performed for the equilibrium included in a coordinate type Cartan subalgebra using the structure of the standard root system of $\mathfrak{so}(n)$. The main result is the linear stability condition for the equilibrium in a coordinate type Cartan subalgebra. Further, a sufficient condition of nonlinear stability is obtained. The case of $SO(4)$ free rigid bodies will be mentioned in detail.

Linear Stability for a Certain Class of Equilibria of an $SO(n)$ Free Rigid Body

Tarama Daisuke

16th July (Fri) 13:30

In this talk, studied is the stability of a certain class of equilibria of an $SO(n)$ free rigid body. The coordinate type Cartan subalgebra in $\mathfrak{so}(n)$ is defined and its characterization is obtained in relation with the Manakov integrals. The stability analysis is performed for the equilibrium included in a coordinate type Cartan subalgebra using the structure of the standard root system of $\mathfrak{so}(n)$. The main result is the linear stability condition for the equilibrium in a coordinate type Cartan subalgebra. Further, a sufficient condition of nonlinear stability is obtained. The case of $SO(4)$ free rigid bodies will be mentioned in detail.