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<p>We study the discretization of (almost-)Dirac structures using the notion of retraction and discretization maps on manifolds. Additionally, we apply the proposed discretization techniques to obtain numerical integrators for port-Hamiltonian systems and we discuss how to merge the discretization procedure and the constraint algorithm associated to systems of implicit differential equations. After fixing a time step, discretization maps are used to discretize the configuration manifold and we obtain different geometric integrators for the given implicit differential equations. As a result we propose a new method that exactly preserves the integrable part of those equations.</p>

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Discretization of Dirac systems and port-Hamiltonian systems: the role of the constraint algorithm

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月23日

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  • María Barbero-Liñán,
  • Juan Manuel López Medel,
  • David Martín de Diego

摘要

We study the discretization of (almost-)Dirac structures using the notion of retraction and discretization maps on manifolds. Additionally, we apply the proposed discretization techniques to obtain numerical integrators for port-Hamiltonian systems and we discuss how to merge the discretization procedure and the constraint algorithm associated to systems of implicit differential equations. After fixing a time step, discretization maps are used to discretize the configuration manifold and we obtain different geometric integrators for the given implicit differential equations. As a result we propose a new method that exactly preserves the integrable part of those equations.