ON THE STABILITY PROBLEM FOR THE $\mathfrak{so}(5)$ FREE RIGID BODY
2011 ◽
Vol 08
(06)
◽
pp. 1205-1223
◽
Keyword(s):
In the general case of the [Formula: see text] free rigid body, we will give a list of integrals of motion, which generate the set of Mishchenko's integrals. In the case of [Formula: see text], we prove that there are 15 coordinate-type Cartan subalgebras which on a regular adjoint orbit give 15 Weyl group orbits of equilibria. These coordinate-type Cartan subalgebras are the analogs of the three axes of equilibria for the classical rigid body on [Formula: see text]. The nonlinear stability and instability of these equilibria is analyzed. In addition to these equilibria there are 10 other continuous families of equilibria.
2013 ◽
Vol 23
(02)
◽
pp. 1350032
◽
1962 ◽
Vol 26
(4)
◽
pp. 914-923
◽
Keyword(s):
1947 ◽
Vol 188
(1015)
◽
pp. 439-463
Keyword(s):
Keyword(s):
1995 ◽
Vol 190
(2)
◽
pp. 373-390
◽