PHASE FLOW OF AN AXIALLY-SYMMETRICAL GYROSTAT WITH ONE CONSTANT ROTOR

We analyze the attitude dynamics of an axially symmetric gyrostat unde r no external forces and one constant internal spin. We introduce coor dinates to represent the orbits of constant angular momentum as a flow on a sphere. With these coordinates, we realize that the problem belo ngs to a general class of Hamiltonian systems, namely the problem here considered is the one parameter Hamiltonian that is a polynomial of a t most degree two in a base of the Lie algebra so (3). The parametric bifurcations are found for both cases, when the rotor is spinning abou t the axis of symmetry of the gyrostat, and when it is spinning about another axis of inertia. The general solution for the global general f low is expressed in terms of the Jacobian elliptic functions. (C) 1997 American Institute of Physics.