Abstract

STRACT
In [2] a new method is suggested for describing the topology of isoenergy surfaces on lie algebra so (4). In
this paper we apply this method for describing the topology of isoenergy surfaces for an integrable case on the lie
algebra so (4).
Study of topology of isoenergetic surfaces in Hamiltonian integrable systems is one of the most important
discussion that relates the physical concepts and topological ones to each other. The topology of isoenergetic
surfaces for classical cases of integrability has been studied by many authors. Such problems are described by
the Euler equations on the Lie algebra e(3). Unfortunately the methods emerged from Euler equations do not
generally apply to the Lie algebra so (4). We apply a new method to solve the problem for an integrable case that
has recently been suggested in [2]. Our extension of this method is based on gluing of bits. In other words at first
we project ,
ℝ() that is called ,
. We describe the topology of ,
. by the polynomial with degree
of three. This manifold is boundary and its components are homeomorphic to closed domains in ℝ(). Through
blowing up these domains, the roots of describing polynomial that is located in domains upboild some cells. By
enumeration of positive roots in every domain, we know that how many cells locate on our discs (bits). At last we
glue these bits symmetrically (that have cells) and rebuild ,ℎ
3 .
