Journal ArticleDOI
On stability of mechanical systems under the action of position forces
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TLDR
In this article, the stability problem for the equilibrium position of a holonomic mechanical system subject to stationary geometric constraints and to potential and non-conservative position forces was solved for the first nonlinear approximation in the absence of degeneracy.About:
This article is published in Journal of Applied Mathematics and Mechanics.The article was published on 1980-01-01. It has received 14 citations till now. The article focuses on the topics: Mechanical equilibrium & Instability.read more
Citations
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Time-reversal symmetry in dynamical systems: a survey
TL;DR: A survey of time-reversal symmetry in dynamical systems can be found in this paper, where the relation of time reversible dynamical sytems to equivariant and Hamiltonian systems is discussed.
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Destabilization paradox due to breaking the Hamiltonian and reversible symmetry
TL;DR: In this paper, the authors studied the stability of a linear autonomous non-conservative system in the presence of potential, gyroscopic, dissipative, and nonconservative positional forces and showed that the boundary of the asymptotic stability domain possesses singularities such as "Dihedral angle" and "Whitney umbrella" that govern stabilization and destabilization.
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Some aspects of destabilization in reversible dynamical systems with application to follower forces
TL;DR: In this article, the destabilization of the equilibria of reversible dynamical systems which is induced by the addition of irreversible perturbations is examined. And the post-destabilization dynamics are also examined using the appropriate normal forms for two specific cases, one where the eigenvalues are non-resonant and the other where they are in a strong one to one resonance.
Journal ArticleDOI
Classical dynamics with curl forces, and motion driven by time-dependent flux
Michael V Berry,Pragya Shukla +1 more
TL;DR: For position-dependent forces whose curl is non-zero, there is no associated scalar potential and therefore no obvious Hamiltonian or Lagrangean and, except in special cases, no obvious conserved quantities as discussed by the authors.
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On the persistence of degenerate lower-dimensional tori in reversible systems
TL;DR: Wang et al. as mentioned in this paper proved that the invariant lower-dimensional torus with given frequency persists under small perturbations, by the Kolmogorov-Arnold-Moser theory and the structure of unperturbed nonlinear terms in the differential equation.
References
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Journal ArticleDOI
Stable and Random Motions in Dynamical Systems
Jürgen Moser,Donald G. Saari +1 more
Journal ArticleDOI
On stability of autonomous systems with internal resonance: PMM vol. 39, n≗ 6, 1975, pp. 974–984
Ia.M. Gol'tser,A.L. Kunitsyn +1 more
TL;DR: In this article, the stability of the trivial solution of an autonomous system of ordinary differential equations in the critical case of n pairs of pure imaginary roots was investigated, where integral linear dependences between the system's frequencies or, in other words, by the internal resonance were examined.