Destabilization paradox due to breaking the Hamiltonian and reversible symmetry

被引:53
作者
Kirillov, Oleg N.
机构
[1] Moscow MV Lomonosov State Univ, Inst Mech, Moscow 119192, Russia
[2] Tech Univ Darmstadt, Dept Mech Engn, Dynam Grp, D-64289 Darmstadt, Germany
关键词
non-conservative system; dissipation-induced instabilities; destabilization paradox;
D O I
10.1016/j.ijnonlinmec.2006.09.003
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
Stability of a linear autonomous non-conservative system in the presence of potential, gyroscopic, dissipative, and non-conservative positional forces is studied. The cases when the non-conservative system is close to a gyroscopic system or to a circulatory one are examined. It is known that marginal stability of gyroscopic and circulatory systems can be destroyed or improved up to asymptotic stability due to action of small non-conservative positional and velocity-dependent forces. The present paper shows that in both cases the boundary of the asymptotic stability domain of the perturbed system possesses singularities such as "Dihedral angle" and "Whitney umbrella" that govern stabilization and destabilization. In case of two degrees of freedom, approximations of the stability boundary near the singularities are found in terms of the invariants of matrices of the system. As an example, the asymptotic stability domain of the modified Maxwell-Bloch equations is investigated with an application to the stability problems of gyroscopic systems with stationary and rotating damping. (C) 2007 Elsevier Ltd. All rights reserved.
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页码:71 / 87
页数:17
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