Nonsmooth Herglotz variational principle

Asier, López-Gordón,; Colombo, Leonardo; León, Manuel de

doi:10.48550/arxiv.2208.02033

Cited by 2 publications

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“…In a future work, we shall provide a variational approach for contact Lagrangian systems with impulsive constraints, extending the variational approach from [28] (see also [16]). Furthermore, we plan to study hybrid contact Hamiltonian and Lagrangian systems.…”

Section: Discussionmentioning

confidence: 99%

Contact Lagrangian systems subject to impulsive constraints

Colombo¹,

León²,

Asier³

2022

J. Phys. A: Math. Theor.

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We describe geometrically contact Lagrangian systems under impulsive forces and constraints, as well as instantaneous nonholonomic constraints which are not uniform along the configuration space. In both situations, the vector field describing the dynamics of a contact Lagrangian system is determined by defining projectors to evaluate the constraints by using a Riemannian metric. In particular, we introduce the Herglotz equations for contact Lagrangian systems subject to instantaneous nonholonomic constraints. Moreover, we provide a Carnot-type theorem for contact Lagrangian systems subject to impulsive forces and constraints, which characterizes the changes of energy due to contact-type dissipation and impulsive forces. We illustrate the applicability of the method with practical examples, in particular, a rolling cylinder on a springily plane and a rolling sphere on a non-uniform plane, both with dissipation.

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Section: Discussionmentioning

confidence: 99%

Contact Lagrangian systems subject to impulsive constraints

Colombo¹,

León²,

Asier³

2022

J. Phys. A: Math. Theor.

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“…In this framework, the action of the mechanical system is added as a variable to the phase space. Through a modification of the principle of least work ( [15], [21], [22]), the modified variational principle outputs trajectories of a dissipative system evolving in a contact manifold [23]. This framework sheds some light on qualitative features possessed by dissipative systems.…”

Section: Introductionmentioning

confidence: 99%

Contracting Forced Lagrangian and Contact Lagrangian Systems: application to nonholonomic systems with symmetries

Simoes¹,

Colombo²

2022

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In this paper we address the problem of identifying contracting systems among dynamical systems appearing in mechanics. First, we introduce a sufficient condition to identify contracting systems in a general Riemannian manifold. Then, we apply this technique to establish that a particular type of dissipative forced mechanical system is contracting, while stating immediate consequences of this fact for the stability of these systems. Finally, we use the previous results to study the stability of particular types of Contact and Nonholonomic systems.

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Nonsmooth Herglotz variational principle

Cited by 2 publications

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Contact Lagrangian systems subject to impulsive constraints

Contact Lagrangian systems subject to impulsive constraints

Contracting Forced Lagrangian and Contact Lagrangian Systems: application to nonholonomic systems with symmetries

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