Phase Portraits of Dynamical Equations of Motion of a Rigid Body in a Resistive Medium

We consider a mathematical model of the influence of a medium on a rigid body with a specific shape of its surface. In this model, we take into account the additional dependence of the moment of the interaction force on the angular velocity of the body. We present a complete system of equations of m...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 233; no. 3; pp. 398 - 425
Main Author Shamolin, M. V.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.09.2018
Springer
Springer Nature B.V
Subjects
Analysis
ANGULAR VELOCITY
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
CYLINDERS
Dependence
EQUATIONS OF MOTION
INTEGRABLE SYSTEMS
INTERACTIONS
MATHEMATICAL METHODS AND COMPUTING
MATHEMATICAL MODELS
Mathematics
Mathematics and Statistics
Portraits
Rigid structures
Rigid-body dynamics
SHAPE
SURFACES
transcendent first integral
quasi-stationarity
integrable system
34Cxx
37N05
37E10
phase portrait
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Summary:We consider a mathematical model of the influence of a medium on a rigid body with a specific shape of its surface. In this model, we take into account the additional dependence of the moment of the interaction force on the angular velocity of the body. We present a complete system of equations of motion under the quasi-stationarity conditions. The dynamical part of equations of motion forms an independent third-order system, which contains, in its turn, an independent secondorder subsystem. We ovtain a new family of phase portraits on the phase cylinder of quasi-velocities, which differs from families obtained earlier.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-018-3935-5