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Topological atlas of the Kowalevski--Yehia gyrostat: analytical results and topological analysis
Mikhail P. Kharlamov, Pavel E. Ryabov, Irina I. Kharlamova +2
We present a review of the results obtained during the last fifty years in the problem of the motion of a heavy gyrostat under the conditions of the Kowalevski type. Hamad M. Yehia…
On the geometry of motions in one integrable problem of the rigid body dynamics
Irina I. Kharlamova, Alexander Yu. Savushkin
Due to Poinsot's theorem, the motion of a rigid body about a fixed point is represented as rolling without slipping of the moving hodograph of the angular velocity over the fixed o…
The electronic atlas of bifurcation diagrams of the Kowalevski-Yehia gyrostat
Irina I. Kharlamova, Pavel E. Ryabov
The integrable case of Kowalevski-Yehia in the dynamics of a gyrostat is considered. We present the new way to classify the bifurcation diagrams of the reduced systems. We find the…
Bifurcation diagrams of the integral mappings of a top with singular symmetry
Alexander Y. Savushkin, Irina I. Kharlamova
In general case, a Hamiltonian system with three degrees of freedom describing the motion of a rigid body in two constant fields does not admit any symmetry groups. H.Yehia has fou…
The existence conditions for periodic motions of the Kowalevski gyrostat in double force field
Irina I. Kharlamova, Gleb E. Smirnov
Consider the integrable problem of motion of a gyrostat with the Kowalevski type inertia tensor in a double force field. We study the special periodic motions (the rank 1 critical…
Bifurcation diagrams on iso-energetic levels of the Kowalevski-Yehia gyrostat
M. P. Kharlamov, I. I. Kharlamova, E. G. Shvedov
We consider the problem of motion of the heavy gyrostat in the case of Kowalevski-Yehia. To classify the bifurcation diagrams on iso-energetic levels we establish the existence of…