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New cases of integrability in dynamics of a rigid body with the cone form of its shape interacting with a medium
Author(s) -
Shamolin Maxim V.
Publication year - 2009
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200910044
Subject(s) - phase portrait , motion (physics) , dynamics (music) , integrable system , rigid body , classical mechanics , rigid body dynamics , physics , flow (mathematics) , cone (formal languages) , phase plane , plane (geometry) , dissipation , mechanics , geometry , mathematical analysis , mathematics , bifurcation , nonlinear system , quantum mechanics , algorithm , acoustics , thermodynamics
The purpose of the activity is to elaborate the qualitative methods for studying the dynamics of rigid bodies interacting with a resisting medium under quasistationarity conditions. This material refers equally to the qualitative theory of ordinary differential equations and the dynamics of rigid bodies. We use the properties of body's motion in a medium under conditions of the jet flow past this body. We study the plane model problems of the motion of a body with the cone form of its shape in a resisting medium. The new families of phase portraits of variable dissipation systems are obtained, their absolute or relative roughness is demonstrated. The integrable cases of equations of motion of rigid bodies are found. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)