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Asymptotic solutions of Lagrangian systems with gyroscopic forces

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Abstract

We consider Lagrangian systems in the presence of nondegenerate gyroscopic forces. The problem of stability of a degenerate equilibrium pointO and the existence of asymptotic solutions is studied. In particular we show that nondegenerate gyroscopic forces in general have, at least formally, a stabilizing effect whenO is a strict maximum point of the potential energy. It turns out that when we switch on arbitrary small nondegenerate gyroscopic forces, a bifurcation phenomenon arises: the instability properties ofO are transferred to a compact invariant set which collapses atO when the gyroscopic forces are switched off.

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Authors and Affiliations

  1. Department of Mathematics and Mechanics, Lomonosov Moscow State University, 119899, Moscow, Russia

    Sergey Bolotin

  2. Dipartmento di Matematica “G. Castelnuovo”, Università di Roma, “La Sapienza”, I 00185, Roma, Italy

    Piero Negrini

Authors
  1. Sergey Bolotin
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  2. Piero Negrini
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Work supported by Russian Fund of Basic Research, the Italian Research Council (CNR) and the Italian Ministery of University (MURST)

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Bolotin, S., Negrini, P. Asymptotic solutions of Lagrangian systems with gyroscopic forces. NoDEA 2, 417–444 (1995). https://doi.org/10.1007/BF01210618

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  • DOI: https://doi.org/10.1007/BF01210618

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