THE CRITICAL TURNING-POINTS IN THE SOLUTIONS OF THE MAGNETIC-TOP EQUATIONS OF MOTION

The solutions of the equations of motion of the magnetic top, whose or ientation is described by the Euler angles curly theta, phi, chi are e xpressed through the integrals of motion and the dependence of their p roperties on these integrals of motion are studied. We find that when the initial canonical momenta p(chi), and p(phi) have equal absolute v alues, the angular velocity curly theta, undergoes a discontinuous cha nge of sign when the turning point of the orbit in curly theta are at the poles (cos curly theta(1), = 1 or cos curly theta(2), = - 1). Thes e discontinuities in curly theta can be compensated by discontinuities in phi and chi (by pi or -pi) so that the linear velocity components of the frame axes are continuous.