The stability of translational motion of a solid with impacts on the horizontal plane

The nonlinear problem on the orbital stability of the periodic motion of a homogeneous paraboloid of revolution above a stationary horizontal plane in a uniform gravitation field is solved. It is assumed that the plane is perfectly smooth and that the impacts of the solid on the plane are perfectly...

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Bibliographic Details
Published inDoklady. a journal of the Russian Academy of Sciences. Physics Vol. 61; no. 2; pp. 87 - 91
Main Authors Markeev, A. P., Sukhoruchkin, D. A.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.02.2016
Subjects
Classical Mechanics
Mathematical and Computational Physics
Mechanics
Physics
Physics and Astronomy
Theoretical
Stationary Point
Translational Motion
Order Resonance
Periodic Motion
Orbital Stability
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Summary:The nonlinear problem on the orbital stability of the periodic motion of a homogeneous paraboloid of revolution above a stationary horizontal plane in a uniform gravitation field is solved. It is assumed that the plane is perfectly smooth and that the impacts of the solid on the plane are perfectly elastic. During unexcited motion, the axis of symmetry of the solid is vertical and the solid moves translationally and periodically encounters the plane. With the method of the Poincare section surfaces the problem is reduced to study of the stability of a stationary point of the self-mapping of the plane, which retains the area. The conditions for stability and instability are obtained for almost all physically permissible values of the parameters of the problem.
ISSN:1028-3358
1562-6903
DOI:10.1134/S1028335816020087