Multicontact formulation for non-conservative field theories

León, Manuel de; Gaset, Jordi; Muñoz, Miguel Luis López-Guadalupe; Rivas, Xavier; Román‐Roy, Narciso

doi:10.1088/1751-8121/acb575

Cited by 8 publications

(2 citation statements)

References 71 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The study of symmetries and dissipated quantities made in this work is the first step towards investigating the symmetries and dissipation laws in non-conservative field theories using the k-(co)contact [20,21,60] and multicontact [61] settings. Furthermore, the classification of symmetries could provide a new insight towards a reduction method for time-(in)dependent contact systems.…”

Section: Conclusion and Further Researchmentioning

confidence: 99%

Symmetries, Conservation and Dissipation in Time‐Dependent Contact Systems

Gaset

Asier

Rivas

2023

Fortschritte der Physik

Self Cite

View full text Add to dashboard Cite

In contact Hamiltonian systems, the so‐called dissipated quantities are akin to conserved quantities in classical Hamiltonian systems. In this article, a Noether's theorem for non‐autonomous contact Hamiltonian systems is proved, characterizing a class of symmetries which are in bijection with dissipated quantities. Other classes of symmetries which preserve (up to a conformal factor) additional structures, such as the contact form or the Hamiltonian function, are also studied. Furthermore, making use of the geometric structures of the extended tangent bundle, additional classes of symmetries for time‐dependent contact Lagrangian systems are introduced. The results are illustrated with several examples. In particular, the two‐body problem with time‐dependent friction is presented, which could be interesting in celestial mechanics.

show abstract

Section: Conclusion and Further Researchmentioning

confidence: 99%

Symmetries, Conservation and Dissipation in Time‐Dependent Contact Systems

Gaset

Asier

Rivas

2023

Fortschritte der Physik

Self Cite

View full text Add to dashboard Cite

show abstract

“…Recently, the contact formulation for non-conservative mechanical systems has been generalised via the so-called k-contact [40,42,55], k-cocontact [69], and multicontact [27,80] formulations. It would be interesting to study the Lie systems whose VG Lie algebra consists of Hamiltonian vector fields relative to these structures.…”

Section: Conclusion and Further Researchmentioning

confidence: 99%

Contact Lie systems: theory and applications

Lucas

Rivas

2023

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

A Lie system is a time-dependent system of differential equations describing the integral curves of a time-dependent vector field that can be considered as a curve in a finite-dimensional Lie algebra of vector fields $V$. We call $V$ a Vessiot--Guldberg Lie algebra.We define and analyse contact Lie systems, namely Lie systems admitting a Vessiot--Guldberg Lie algebra of Hamiltonian vector fields relative to a contact manifold. We also study contact Lie systems of Liouville type, which are invariant relative to the flow of a Reeb vector field. Liouville theorems, contact Marsden--Weinstein reductions, and Gromov non-squeezing theorems are developed and applied to contact Lie systems. Contact Lie systems on three-dimensional Lie groups with Vessiot--Guldberg Lie algebras of right-invariant vector fields and associated with left-invariant contact forms are classified. Our results are illustrated by examples with relevant physical and mathematical applications, e.g. Schwarz equations, Brockett systems, quantum mechanical systems, etc. Finally, a Poisson coalgebra method to derive superposition rules for contact Lie systems of Liouville is developed.

show abstract