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

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Abstract

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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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Bari “A. Moro”, Via E. Orabona 4, 70125, Bari, Italy

    Anna Maria Candela

  2. Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain

    Alfonso Romero & Miguel Sánchez

Authors
  1. Anna Maria Candela
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  2. Alfonso Romero
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  3. Miguel Sánchez
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Correspondence to Anna Maria Candela.

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Communicated by P. Rabinowitz

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Candela, A.M., Romero, A. & Sánchez, M. Completeness of the Trajectories of Particles Coupled to a General Force Field. Arch Rational Mech Anal 208, 255–274 (2013). https://doi.org/10.1007/s00205-012-0596-2

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  • DOI: https://doi.org/10.1007/s00205-012-0596-2

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