The geometric formulation of Hamilton--Jacobi theory for systems with nonholonomic constraints is developed, following the ideas of the authors in previous papers. The relation between the solutions of the Hamilton--Jacobi ...

This paper introduces a novel geometric framework to define and study hybrid systems. We exploit the geometry and topology of the set of jump points, where the instantaneous change of dynamics takes place, in order to gain ...

We present a new setting of the geometric Hamilton-Jacobi theory by using the so-called time-evolution operator K. This new approach unifies both the Lagrangian and the Hamiltonian formulation of the problem developed in ...

We present a complete theory of higher-order autonomous contact mechanics, which allows us to describe higher-order dynamical systems with dissipation. The essential tools for the theory are the extended higher-order tangent ...

A geometric approach to Sundman infnitesimal time-reparametrisation is given and some of its applications are used to illustrate the general theory. Special emphasis is put on geodesic motions and systems described by ...

We provide new insights into the contact Hamiltonian and Lagrangian formulations of dissipative mechanical systems. In particular, we state a new form of the contact dynamical equations, and we review two recently presented ...

Pontryagin’s Maximum Principle [8] is considered as an outstanding achievement of optimal control theory. This Principle does not give sufficient conditions to compute an optimal trajectory; it only provides necessary ...

Esta obra intenta dar una visión de la evolución histórica del cálculo infinitesimal: Los problemas originales en el siglo XVII, la aportación realizada por Newton y Leibnitz que consistió fundamentalmente en efectuar una ...