WIAS Preprint No. 1662, (2011)

The elliptic-regularization principle in Lagrangian mechanics


  • Liero, Matthias
    ORCID: 0000-0002-0963-2915
  • Stefanelli, Ulisse

2010 Mathematics Subject Classification

  • 70H03 70H30 65L10


  • Lagrangian mechanics, variational principle, elliptic regularization, time discretization




We present a novel variational approach to Lagrangian mechanics based on elliptic regularization with respect to time. A class of parameter-dependent global-in-time minimization problems is presented and the convergence of the respective minimizers to the solution of the system of Lagrange's equations is ascertained. Moreover, we extend this perspective to mixed dissipative/nondissipative situations, present a finite time-horizon version of this approach, and provide related Γ-convergence results. Finally, some discussion on corresponding time-discrete versions of the principle is presented.

Appeared in

  • J. Nonlinear Sci., 23 (2013) pp. 179--204, under the title "A new minimum principle for Lagrangian mechanics"

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