In this paper, we apply the geometric Hamilton–Jacobi theory to obtain solutions of classical
hamiltonian systems that are either compatible with a cosymplectic or a contact structure. As …

This paper contains a fully geometric formulation of the General Equation for Non-
Equilibrium Reversible-Irreversible Coupling (GENERIC). Although GENERIC, which is the …

This book is devoted to review two of the most relevant approaches to the study of classical
field theories of the first order, say k-symplectic and k-cosymplectic geometry. This approach …

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 …

In this paper, we study the integrability of contact Hamiltonian systems, both time-dependent
and independent. In order to do so, we construct a Hamilton–Jacobi theory for these systems …

This work is devoted to review the modern geometric description of the Lagrangian and
Hamiltonian formalisms of the Hamilton–Jacobi theory. The relation with the “classical” …

The nonholonomic dynamics can be described by the so-called nonholonomic bracket on
the constrained submanifold, which is a non-integrable modification of the Poisson bracket …

The aim of this paper is to present a short historical/scientific review on nonholonomic
mechanics, with special emphasis on the latest developments. Indeed, the use of differential …

The main focus is on the Hamilton–Jacobi techniques in classical general relativity that were
pursued by Peter Bergmann and Arthur Komar in the 1960s and 1970s. They placed special …

Abstract We develop Hamilton–Jacobi theory for Chaplygin systems, a certain class of
nonholonomic mechanical systems with symmetries, using a technique called …