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On destabilizing effects of two fundamental non-conservative forces

Krechetnikov, R. and Marsden, J. E. (2006) On destabilizing effects of two fundamental non-conservative forces. Physica D, 214 (1). pp. 25-32. ISSN 0167-2789. doi:10.1016/j.physd.2005.12.003.

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In this work we discuss the instabilities in mechanical systems caused by two fundamentally different non-conservative forces, referred to as dissipative and positional forces, each of which may lead to energy dissipation. One of the objectives of this discussion is to recall and to put into the context of current research some of the important classical results by Thomson–Tait–Chetayev and Merkin, which are under-appreciated nowadays: many new examples, e.g. radiation in Hamiltonian systems, the Levitron, etc., appearing in recent literature can be interpreted with the help of these classical results. Next, in the spirit of the Lagrange–Dirichlet theory, we introduce the geometric picture of the phase space corresponding to the effects of destabilization in finite-dimensional systems. On the physical side, our objective is to demonstrate that both of these types of non-conservative forces appear quite commonly and often simultaneously in physical systems. As an illustration, we consider the Levitron, a system in which the dissipative effects have not heretofore been studied. Finally, using Nikolai’s elastic bar model as a paradigm, we discuss the notion of a secondary dissipation-induced instability, when the above two fundamental non-conservative forces interact. This unified way of thinking should help us to understand the intricate links among various mechanical systems through the most fundamental mechanisms in their behavior

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Additional Information:© 2005 Elsevier Ltd All rights reserved. Received 1 June 2005; received in revised form 15 November 2005; accepted 9 December 2005. Communicated by J. Lega. This research was partially supported by NSF-ITR Grant ACI-0204932. The authors also thank Nawaf Bou-Rabee for bringing his work [24] to our attention and for a stimulating discussion.
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Subject Keywords:Classical mechanics; Dissipation; Positional forces; Instabilities
Issue or Number:1
Record Number:CaltechAUTHORS:20100820-095943544
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19550
Deposited By: Ruth Sustaita
Deposited On:20 Aug 2010 18:48
Last Modified:08 Nov 2021 23:53

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