Abstract

We give an existence result for the dynamics of a system of particles moving on a line in a horizontal plane and subjected to friction, to percussional effects, to stiffness and to damping. The novelty in our study is that the normal reaction is expressed by a measure, incorporating a series of Dirac measures. The velocity is a function of bounded variation and the acceleration is its Stieltjes measure. Together with the tangential reaction — which is also a measure — they must satisfy a measure-differential inclusion formulation of friction. Convex analysis, variational inequalities and measure theory are used in the existence proof.

Author information

Contact details are reproduced from the original publication and may be historical.

M. Laghdir

Faculté des Sciences, Rabat, Maroc.

Manuel D. P. Monteiro Marques

Centro de Matemática e Aplicações Fundamentais, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1699 Lisboa Codex, Portugal

Keywords

  • Particle dynamics
  • normal percussions
  • bounded variation
  • measure-differential inclusions

References

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Suggested citation

M. Laghdir, M. D. P. Monteiro Marques. “Measure-Differential Inclusions in Percussional Dynamics.” Journal of Convex Analysis 4 (1997), No. 2, 381–393. https://doi.org/10.68381/jca04023

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Published by Heldermann Verlag, 1997. Rights now held by Banach Press.