The inverse problem in the calculus of variations and the geometry of the tangent bundle

G Morandi, C Ferrario, GL Vecchio, G Marmo… - Physics Reports, 1990 - Elsevier
The present paper deals with the geometry of the tangent bundle over a differentiable (Cr)
manifold, and with the so-called inverse problem of Lagrangian dynamics. There are various …

[HTML][HTML] Infinitesimal symmetries in contact Hamiltonian systems

M de León, ML Valcázar - Journal of Geometry and Physics, 2020 - Elsevier
In this paper, we extend the well-known Noether theorem for Lagrangian systems to contact
Lagrangian systems. We introduce a classification of infinitesimal symmetries and obtain the …

Symmetries, Conservation and Dissipation in Time‐Dependent Contact Systems

J Gaset, A López‐Gordón, X Rivas - Fortschritte der Physik, 2023 - Wiley Online Library
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 …

Variational principles for nonpotential operators

VM Filippov, VM Savchin, SG Shorokhov - Journal of Mathematical …, 1994 - Springer
One presents numerous approaches for the construction of variational principles for
equations with operators which, in general, are nonpotential. One considers separately …

Symmetries, constants of the motion, and reduction of mechanical systems with external forces

M De León, M Lainz, A López-Gordón - Journal of Mathematical …, 2021 - pubs.aip.org
This paper is devoted to the study of mechanical systems subjected to external forces in the
framework of symplectic geometry. We obtain Noether's theorem for Lagrangian systems …

The geometry of dissipation

A López-Gordón - arxiv preprint arxiv:2409.11947, 2024 - arxiv.org
Dissipative phenomena manifest in multiple mechanical systems. In this dissertation,
different geometric frameworks for modelling non-conservative dynamics are considered …

Jacobi fields and linear connections for arbitrary second-order ODEs

M Jerie, GE Prince - Journal of Geometry and Physics, 2002 - Elsevier
Jacobi fields and linear connections for arbitrary second-order ODEs - ScienceDirect Skip to
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Symmetries and constants of the motion for higher‐order Lagrangian systems

M de León, DM de Diego - Journal of Mathematical Physics, 1995 - pubs.aip.org
We obtain a classification of infinitesimal symrnetties of an autonomous higherorder
Lagrangian system by using the theory of lifts of vector fields to tangent bundles. Also, a …

Symmetries in vakonomic dynamics: applications to optimal control

S Martínez, J Cortés, M De León - Journal of Geometry and Physics, 2001 - Elsevier
Symmetries in vakonomic dynamics are discussed. Appropriate notions are introduced and
their relationship with previous work on symmetries of singular Lagrangian systems is …

Some contributions to k-contact Lagrangian field equations, symmetries and dissipation laws

X Rivas, M Salgado, S Souto - arxiv preprint arxiv:2304.00833, 2023 - arxiv.org
It is well known that k-contact geometry is a suitable framework to deal with non-
conservative field theories. In this paper, we study some relations between solutions of the k …