On the stability of nonconservative systems with small dissipation

Journal of Mathematical Sciences

Volumn 145, Issue 5, 2007, Pages 5260-5270

  Kirillov, O N ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34548680085     PISSN: 10723374     EISSN: 15738795     Source Type: Journal    
DOI: 10.1007/s10958-007-0351-7     Document Type: Article

References (17)

1. V. I. Arnol'd, Supplementary Chapters of Theory of Ordinary Differential Equations [in Russian], Nauka, Moscow (1978).
2. S. Barnett, "Leverrier's algorithm: A new proof and extensions," SIAM J. Matrix Anal. Appl., 10, No. 4, 551-556 (1989).
3. H. Bilharz, "Bemerkung zu einem Satze von Hurwitz," Z. Angew. Math. Mech., 24, 77-82 (1944).
4. V. V. Bilitin, Nonconservative Problems of Elastic Stability Theory [in Russian], Fizmatgiz, Moscow (1961).
5. A. M. Bloch, P. S. Krishnaprasad, J. E. Marsden, and T. S. Ratiu, "Dissipation induces instabilities," Ann. Inst. H. Poincaré, 11, No. 1, 37-90 (1994).
6. V. V. Bolotin and N. I. Zhinzher, "Effects of damping on stability of elastic systems subjected to nonconservative forces," Int. J. Solids Structures, 5, 965-989 (1969).
7. V. I. Gugnina, "Extension of the D. K. Faddeev method to polynomial matrices," Dokl. Akad. Nauk UzSSR, 1, 5-10 (1958).
8. O. N. Kirillov, "Destabilization paradox," Dokl. Ross. Akad. Nauk, 395, No. 5, 614-620.
9. K. Popp, M. Rudolph, M. Kroger, and M. Lindner, "Mechanisms to generate and to avoid friction induced vibrations," in: VDI-Berichte, No. 1736 (2002).
10. A. P. Seiranyan, "Destabilization paradox in the stability problems of nonconservative systems," Usp. Mekh., 13, No. 2, 89-124 (1990).
11. A. P. Seiranyan, "On stabilization of nonconservative systems by dissipative forces and indeterminacy of the critical loading," Dokl. Ross. Akad. Nauk, 348, No. 3, 323-326 (1996).
12. A. P. Seiranyan and O. N. Kirillov, "On the influence of small dissipative and gyroscopic forces on the stability of nonconservative systems," Dokl. Ross Akad. Nauk, 393, No. 4, 483-488 (2003).
13. A. P. Seyranian and O. N. Kirillov, "Bifurcation diagrams and stability boundaries of circulatory systems," Theor. Appl. Mech., 26, 135-168 (2001).
14. A. P. Seyranian and A. A. Mailybaev, Multiparameter Stability Theory with Mechanical Applications, World Scientific, Singapore (2003).
15. M. I. Vishik and L. A. Lyusternik, "Solution of some perturbation problems in the case of matrices and self-adjoint and non-self-adjoint differential equations, I," Usp. Mat. Nauk, 15, No. 3, 3-80 (1960).
16. N. I. Zhinzher, "Influence of dissipative forces with incomplete dissipation on the stability of elastic systems," Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, 19, No. 1, 149-155, (1994).
17. H. Ziegler, "Die Stabilitatskriterien der Elastomechanik," Ing.-Arch., 20, 49-56 (1952).