The Herglotz principle and vakonomic dynamics
Document typeConference lecture
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In this paper we study vakonomic dynamics on contact systems with nonlinear constraints. In order to obtain the dynamics, we consider a space of admisible paths, which are the ones tangent to a given submanifold. Then, we find the critical points of the Herglotz action on this space of paths. This dynamics can be also obtained through an extended Lagrangian, including Lagrange multiplier terms. This theory has important applications in optimal control theory for Herglotz control problems, in which the cost function is given implicitly, through an ODE, instead of by a definite integral. Indeed, these control problems can be considered as particular cases of vakonomic contact systems, and we can use the Lagrangian theory of contact systems in order to understand their symmetries and dynamics.
The final publication is available at https://link.springer.com/chapter/10.1007/978-3-030-80209-7_21#citeas
CitationMuñoz-Lecanda, M.C.; De León, M.; Lainz, M. The Herglotz principle and vakonomic dynamics. A: "Geometric science of information: 5th International Conference, GSI 2021, Paris, France, July 21-23, 2021: proceedings". Springer Nature, 2021, p. 183-190. ISBN 978-3-030-80208-0. DOI 10.1007/978-3-030-80209-7_21.