The problem of the motion, of a rigid body around a fixed point, in the field of constant gravity, is one of the oldest in mechanics [1,2,3]. The problem can be formulated in terms of a timeindependent Hamiltonian with three degrees of freedom (the Euler angles. In addition to the energy constant, there is present another constant of motion: the angular momentum component along the vertical. Ro...

We develop certified tracking procedures for Newton homotopies, which are homotopies for which only the constant terms are changed. For these homotopies, our certified procedures include using a constant predictor with Newton corrections, an Euler predictor with no corrections, and an Euler predictor with Newton corrections. In each case, the predictor is guaranteed to produce a point in the qu...