Archive for Rational Mechanics and Analysis

, Volume 208, Issue 1, pp 255–274 | Cite as

Completeness of the Trajectories of Particles Coupled to a General Force Field

  • Anna Maria Candela
  • Alfonso Romero
  • Miguel Sánchez


We analyze the extendability of the solutions to a certain second order differential equation on a Riemannian manifold (M, g), which is defined by a general class of forces (both prescribed on M or depending on the velocity). The results include the general time-dependent anholonomic case, and further refinements for autonomous systems or forces derived from a potential are obtained. These extend classical results for Lagrangian and Hamiltonian systems. Several examples show the optimality of the assumptions as well as the utility of the results, including an application to relativistic pp-waves.


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Anna Maria Candela
    • 1
  • Alfonso Romero
    • 2
  • Miguel Sánchez
    • 2
  1. 1.Dipartimento di MatematicaUniversità degli Studi di Bari “A. Moro”BariItaly
  2. 2.Departamento de Geometría y Topología, Facultad de CienciasUniversidad de GranadaGranadaSpain

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