Bifurcation Diagram of the Model of a Lagrange Top with a Vibrating Suspension Point

The article considers a model system that describes a dynamically symmetric rigid body in the Lagrange case with a suspension point that performs high-frequency oscillations. This system, reduced to axes rigidly connected to the body, after the averaging procedure, has the form of the Hamilton equations with two degrees of freedom and has the Liouville integrability property of a Hamiltonian system with two degrees of freedom, which describes the dynamics of a Lagrange top with an oscillating suspension point. The paper presents a bifurcation diagram of the moment mapping. Using the bifurcation diagram, we presented in geometric form the results of the study of the problem of stability of singular points, in particular, singular points of rank zero and rank one.

Automated summary

The article examines a model system of a dynamically symmetric rigid body with a suspension point that oscillates at high frequency. After the averaging process, the system is reduced to Hamilton equations with two degrees of freedom, exhibiting Liouville integrability, which describes the dynamics of a Lagrange top with an oscillating suspension point. The paper presents a bifurcation diagram of the moment mapping and uses it to illustrate the stability analysis of singular points, including rank zero and rank one.