Dynamical systems with variable dissipation: approaches, methods, and applications
type: Item
instance of: scholarly article
title: Dynamical systems with variable dissipation: approaches, methods, and applications
zbMATH Open document ID: 1189.37022
author: M. V. Shamolin
published in: Journal of Mathematical Sciences (New York)
publication date: 2010-01-19T00:00:00Z
review text: The main results of this works are as follows: 1. To present a relatively simple methodology for finding dimensionless parameters of the medium action on a rigid body under the quasi-stationarity conditions, which is successfully applied for studying the motion of bodies having a simple form, the circular cylinders entering the water. 2. To elaborate new qualitative methods for studying variable dissipation systems. Obtained the conditions for the existence of the bifurcation of stable and unstable auto-oscillation birth. Presented the conditions for the absence of such trajectories. The theory of Poincare plane topographical systems and comparison systems is extended to the spatial case. A sufficiently simple methodology for proving the Poisson stability of unclosed trajectories of dynamical systems is presented. The definitions of relatively structural stability and relative structural instability of various degrees are introduced. 3. New integrable cases and families of phase portraits in the plane rigid body dynamics are discovered. Some model variants of the body motion in a resisting medium are qualitatively studied and have been integrated. It is shat the first integrals of the corresponding systems are transcendental functions and that are expressed through elementary functions. New two-parameter families of topologically nonequivalent phase portraits are constructed. 4. New integrable cases and families of many-dimensional phase portraits in the spatial rigid body dynamics are discovered. A new two-parameter family of phase portraits in the problem of the spatial free drag of a body is obtained.
Mathematics Subject Classification ID: 37C15
Mathematics Subject Classification ID: 34D30
zbMATH DE Number: 5660185
zbMATH Keywords: dynamical systems
zbMATH Keywords: Poincaré topographic systems
zbMATH Keywords: rigid body
MaRDI profile type: Publication
full work available at URL: s10958-009-9657-y
OpenAlex ID: W2028616958
cites work: Generation of limit cycles from a separatrix forming a loop and from the separatrix of an equilibrium state of saddle-node type
cites work: Q5518664
cites work: Q5553435
cites work: Q5582924
cites work: Q5566243
cites work: Q4774386
cites work: Topological classification of flows on closed two-dimensional manifolds
cites work: Q3993170
cites work: A method of stabilizing third-order control systems with large gains. II
cites work: Q5832271
cites work: Q5654424
cites work: Certain qualitative investigation methods for dynamic systems connected with field rotation
cites work: Q3992468
cites work: Q3200292
cites work: Q4077489
cites work: First integrals of systems with gyroscopic forces
cites work: Q3881925
cites work: Q4761702
cites work: Q5662607
cites work: Q3333762
cites work: Q3961135
cites work: Q3733030
cites work: On the motion of a solid in a magnetic field
cites work: Supramenability and the problem of occurrence of free semigroups
cites work: Intersection of asymptotic surfaces of the perturbed Euler-Poinsot problem
cites work: Splitting of separatrices for unstable uniform rotations and nonintegrability of perturbed Lagrange problem
cites work: Q3719516
cites work: Q4743093
cites work: Q3314608
cites work: On the stability of the equilibrium positions for discontinuous systems
cites work: Q3372945
cites work: Q3657585
cites work: Q5797273
cites work: Q5819974
cites work: Q3285630
cites work: Q3282146
cites work: Q5517953
cites work: On the existence of flow of a heavy perfect fluid in a channel with a sloping bottom
cites work: Euler equations in models of theoretical physics
cites work: Q4177020
cites work: Q3221462
cites work: Q3345936
cites work: Vortex theory of a top
cites work: Q3856167
cites work: Q3327769
cites work: Q5523404
cites work: Q3271991
cites work: Q5605814
cites work: On the structure of optimal trajectories of motion of a rotating body in a resting medium
cites work: Q3231426
cites work: Q5588449
cites work: Q5657709
cites work: Q3264374
cites work: On structural stability
cites work: Structural stability on two-dimensional manifolds
cites work: On an approximation theorem of Kupka and Smale
cites work: p-adic analog of the Kazhdan-Lusztig hypothesis
cites work: Q3275124
cites work: Q5345170
cites work: Q5584120
cites work: Q3909341
cites work: Q3885243
cites work: Q5639680

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cites work: Body motion in a resisting medium

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cites work: Q3334584

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cites work: Phase pattern classification for the problem of the motion of a body in a resisting medium in the presence of a linear damping moment

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cites work: Q3364177

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cites work: The definition of relative robustness and a two-parameter family of phase portraits in the dynamics of a rigid body

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cites work: Introduction to problem on braking of a body in a resisting medium and new two-parametric family of phase portraits

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cites work: Q4386687

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cites work: Spatial topographical systems of Poincaré and comparison systems

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cites work: On integrability in transcendental functions

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cites work: New integrable, in the sense of Jacobi, cases in the dynamics of a rigid body interacting with a medium.

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cites work: Robustness of dissipative systems and relative robustness and non-robustness of systems with variable dissipation

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cites work: On limit sets of differential equations near singular critical points

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cites work: Q4787045

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cites work: Some questions of the qualitative theory of ordinary differential equations and dynamics of a rigid body interacting with a medium

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cites work: Foundations of differential and topological diagnostics

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cites work: New integrable cases and families of portraits in the plane and spatial dynamics of a rigid body interacting with a medium

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cites work: Classes of variable dissipation systems with nonzero mean in the dynamics of a rigid body

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cites work: Geometrical Representation of the Motion of a Body Through a Medium

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cites work: Q3412305

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cites work: A case of complete integrability in the dynamics on the tangent bundle of a two-dimensional sphere

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cites work: Methods of analysis of various dissipation dynamical systems in dynamics of a rigid body

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cites work: Q3541439

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cites work: Three-parametric family of phase portraits in dynamics of a solid interacting with a medium

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cites work: Q5605744

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cites work: Q3271346

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cites work: Asymptotic Theory of Separated Flows

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cites work: Q3343473

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cites work: Q3897220

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cites work: Symplectic structures on groups of automorphisms of symmetric spaces

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cites work: Q3943706

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cites work: Dynamics of a body with a fluid-filled ellipsoidal cavity

Dynamical systems with variable dissipation: approaches, methods, and applications (DOI)
DOI: 10.1007/S10958-009-9657-Y