Related papers: Contact Hamiltonian systems with nonholonomic cons…
We show that some modern geometric methods of Hamiltonian dynamics can be directly applied to the nonholonomic Heisenberg type systems. As an example we present characteristic Killing tensors, compatible Poisson brackets, Lax matrices and…
We approach the analysis of dynamical and geometrical properties of nonholonomic mechanical systems from the discussion of a more general class of auxiliary constrained Hamiltonian systems. The latter is constructed in a manner that it…
Contact geometry allows to describe some thermodynamic and dissipative systems. In this paper we introduce a new geometric structure in order to describe time-dependent contact systems: cocontact manifolds. Within this setting we develop…
A hybrid system is a system whose dynamics is given by a mixture of both continuous and discrete transitions. In particular, these systems can be utilised to describe the dynamics of a mechanical system with impacts. Based on the approach…
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 of the ambient space, in this case, of the canonical bracket on…
This paper considers systems subject to nonholonomic constraints which are not uniform on the whole configuration manifold. When the constraints change, the system undergoes a transition in order to comply with the new imposed conditions.…
In this paper, we develop a Hamiltonian variational formulation for the nonequilibrium thermodynamics of simple adiabatically closed systems that is an extension of Hamilton's phase space principle in mechanics. We introduce the…
Nonholonomic mechanical systems have been attracting more interest in recent years because of their rich geometric properties and their applications in Engineering. In all generality, we discuss the reduction of a Hamilton-Jacobi theory for…
We consider a simple motivating example of a non-Hamiltonian dynamical system with time-dependent constraints obtained by imposing rheonomic non-integrable Bilimovich's constraint on a freely rotating rigid body. Dynamics of this…
This paper presents a geometric description of Lagrangian and Hamiltonian systems on Lie affgebroids subject to affine nonholonomic constraints. We define the notion of nonholonomically constrained system, and characterize regularity…
We propose a simple construction of the non-Hamiltonian dynamical systems possessing an invariant measure. These non-Hamiltonian systems are deformations of the Hamiltonian systems associated with trivial deformations of the canonical…
A convenient algebraic structure to describe some forms of dynamics of two hamiltonian systems with nonpotential (magnetic--type) interaction is considered. An algebraic mechanism of generation of such dynamics is explored on simple "toy"…
A universal algorithm to derive a macroscopic dynamics from the microscopic dynamical system via the averaging process and symplecto-contact reduction was introduced by Jin-wook Lim and the second-named author in [LO23]. They apply the…
There has been increasing interest in methodologies that incorporate physics priors into neural network architectures to enhance their modeling capabilities. A family of these methodologies that has gained traction are Hamiltonian neural…
Contact Hamiltonian dynamics is a subject that has still a short history, but with relevant applications in many areas: thermodynamics, cosmology, control theory, and neurogeometry, among others. In recent years there has been a great…
In this paper we study Hamiltonian systems on contact manifolds, which is an appropriate scenario to discuss dissipative systems. We prove a coisotropic reduction theorem similar to the one in symplectic mechanics.
This paper studies hamiltonization of nonholonomic systems using geometric tools. By making use of symmetries and suitable first integrals of the system, we explicitly define a global 2-form for which the gauge transformed nonholonomic…
Stochastic contact Hamiltonian systems are a class of important mathematical models, which can describe the dissipative properties with odd dimensions in the stochastic environment. In this article, we investigate the numerical dynamics of…
We prove that certain non-exact magnetic Hamiltonian systems on products of closed hyperbolic surfaces and with a potential function of large oscillation admit non-constant contractible periodic solutions of energy below the Ma\~n\'e…
Virtual constraints are relations imposed on a control system that become invariant via feedback control, as opposed to physical constraints acting on the system. Nonholonomic systems are mechanical systems with non-integrable constraints…