Related papers: Higher-order contact mechanics
We discuss an elementary derivation of variational symmetries and corresponding integrals of motion for the Lagrangian systems depending on acceleration. Providing several examples, we make the manuscript accessible to a wide range of…
In this paper an approach is proposed to represent a class of dissipative mechanical systems by corresponding infinite-dimensional Hamiltonian systems. This approach is based upon the following structure: for any non-conservative classical…
Reparametrization invariant Lagrangian theories with higher derivatives are considered. We investigate the geometric structures behind these theories and construct the Hamiltonian formalism in a geometric way. The Legendre transformation…
We develop a unified geometric framework for mechanical systems that combine conservative and dissipative dynamics by formulating them on contact manifolds. Within this setting, we identify the Reeb vector field as the intrinsic generator…
This work explores the tensor and combinatorial constructs underlying the linearised higher-order variational equations of a generic autonomous system along a particular solution. The main result of this paper is a compact yet explicit and…
We develop a new, coordinate-free formulation of Hamiltonian mechanics on the dual of a Lie algebroid. Our approach uses a connection, rather than coordinates in a local trivialization, to obtain global expressions for the horizontal and…
We consider solutions of Lagrangian variational problems with linear constraints on the derivative. These solutions are given by curves $\gamma$ in a differentiable manifold $M$ that are everywhere tangent to a smooth distribution $\mathcal…
The notion of global higher-form symmetries has received much attention, but leaves room for a more systematic mathematical formulation. In this article, we highlight the concept of higher automorphism bundles from the field of higher…
A method to construct a geometric structure with the same solutions as a given variational principle is presented. The method applies to large families of variational principles. In particular, the known results that assign cosymplectic…
By introducing an integration factor to the differential one-form of contact dynamics, equations of motion are derived variationally, and contact Poisson bracket and contact Lagrangian are formulated. Discrete symplectic integrator, named…
This sequel to our previous paper [MS11b] continues the study of topological contact dynamics and applications to contact dynamics and topological dynamics. We provide further evidence that the topological automorphism groups of a contact…
We introduce a new geometric framework for relativistic particle dynamics based on contact geometry and suitable for treating dissipative processes like particle decay. The dynamics is formulated on a nine--dimensional extended phase space…
The aim of this paper is to propose an unambiguous intrinsic formalism for higher-order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, which implies the existence of…
Most of the engineering and physical systems are generally characterized by differential and difference equations based on their continuous-time and discrete-time dynamics, respectively. Moreover, these dynamical models are analyzed using…
We develop a reduction theory for $G$-invariant Lagrangian field theories defined on the higher-order jet bundle of a principal $G$-bundle, thus obtaining the higher-order Euler-Poincar\'e field equations. To that end, we transfer the…
The EHP and the MCAP provide new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics. Both approaches utilize the mixed formulation and lead to the development of…
We present a picture of Lagrangean mechanics, free of some unnatural features (such as complete divergences). As a byproduct, a completely natural U(1)-bundle over the phase space appears. The correspondence between classical and quantum…
The aim of this work is to study the geometry underlying mechanics and its application to describe autonomous and nonautonomous conservative dynamical systems of different types; as well as dissipative dynamical systems. We use different…
Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…
Action-dependent field theories are systems where the Lagrangian or Hamiltonian depends on new variables that encode the action. They model a larger class of field theories, including non-conservative behavior, while maintaining a…