Contact Hamiltonian dynamics is a subject that has still a short history, but with relevant
applications in many areas: thermodynamics, cosmology, control theory, and …

In this survey, we review the classical Hamilton–Jacobi theory from a geometric point of view
in different geometric backgrounds. We propose a Hamilton–Jacobi equation for different …

This booklet studies the geometry of the reduction of Lagrangian systems with symmetry in a
way that allows the reduction process to be repeated; that is, it develops a context for …

Nonholonomic systems are a widespread topic in several scientific and commercial
domains, including robotics, locomotion and space exploration. This work sheds new light …

The purpose of this paper is to show that the method of controlled Lagrangians and its
Hamiltonian counterpart (based on the notion of passivity) are equivalent under rather …

This paper outlines some features of general reduction theory as well as the geometry of
nonholonomic mechanical systems. In addition to this survey nature, there are some new …

In this paper, we discuss the singular Lagrangian systems on the framework of contact
geometry. These systems exhibit a dissipative behavior in contrast with the symplectic …

In this paper, we study the underlying geometry in the classical Hamilton-Jacobi equation.
The proposed formalism is also valid for nonholonomic systems. We first introduce the …

This paper presents a geometric description on Lie algebroids of Lagrangian systems
subject to nonholonomic constraints. The Lie algebroid framework provides a natural …

A nonholonomic system, for short “NH,” consists of a configuration space Q n, a Lagrangian
L (q, ̇ q, t), a nonintegrable constraint distribution H ⊂ TQ, with dynamics governed by …