Discrete dynamics of complexbodies with substructural dissipation: Variational integrators andconvergence

Matteo Focardi; Paolo Maria Mariano

doi:10.3934/dcdsb.2009.11.109

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2009, Volume 11, Issue 1: 109-130. Doi: 10.3934/dcdsb.2009.11.109

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Discrete dynamics of complex bodies with substructural dissipation: Variational integrators and convergence

Matteo Focardi^1, and
Paolo Maria Mariano^2,

1.
Dipartimento di Matematica "U. Dini", Università di Firenze, viale Morgagni 67/A, I-50139 Firenze
2.
DICeA, Università di Firenze, via Santa Marta 3, I-50139 Firenze

Received: November 30, 2007

Revised: February 29, 2008

Published: June 2009

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Abstract

For the linearized setting of the dynamics of complex bodies we construct variational integrators and prove their convergence by making use of BV estimates on the rate fields. We allow for peculiar substructural inertia and internal dissipation, all accounted for by a d'Alembert-Lagrange-type principle.

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Mathematics Subject Classification: Primary: 37M15, 74A30, 74A99.

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