Bifurcation diagrams involving the linear integral of Yehia

Abstract

In the general case the Hamiltonian system with three degrees of freedom describing the motion of a rigid body in two constant forces does not admit any symmetry groups. Yehia (1986 Mech. Res. Commun. 13 169-72) found conditions under which the equations of motion of the Kowalevski-type top have an integral linear in angular velocities in addition to the energy integral. Later it was noticed that such an integral exists for the same force field for any dynamically symmetric top with the center of force applications in the equatorial plane. Thus, the corresponding system is the natural mechanical system with S 1 -symmetry and Smale's program of topological analysis can be fulfilled. Here we construct the bifurcation diagrams of the momentum map for this system and present various types of diagrams depending on one physical parameter.

Bifurcation analysis of nonlinear Hamiltonian dynamics in the Fermilab Integrable Optics Test Accelerator

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