A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Paper connects dynamics of mechanical systems to Reeb dynamics.
This work generalizes Hamiltonian mechanics using closed differential forms.
A new description, different by the classical theory of Hamiltonian Mechanics, in the general framework of generalized Lie algebroids is presented. In the particular case of Lie algebroids, new and important results are obtained. We present the \emph{dual mechanical systems} called by use, \emph{dual mechanical}$(ρ,η) …
The paper extends Marsden-Weinstein reduction to mechanical presymplectic structures for time-dependent Hamiltonian systems.
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 mechanical system and arbitrary initial conditions, there exists a conservative …
The application of the Legendre transformation to a hyperregular Lagrangian system results in a Hamiltonian vector field generated by a Hamiltonian defined on the phase space of the mechanical system. The Legendre transformation in its usual interpretation can not be applied to homogeneous Lagrangians found in relativi…
Paper presents a new port-Hamiltonian model for vehicle manipulators.
This paper extends the evolution operator to contact mechanics, linking Lagrangian and Hamiltonian formulations.
Studies geometric mechanics for autonomous and nonautonomous systems.
The aim of the present text is twofold: to provide a compendium of Lagrangian and Hamiltonian geometries and to introduce and investigate new analytical Mechanics: Finslerian, Lagrangian and Hamiltonian. The fundamental equations (or evolution equations) of these Mechanics are derived from the variational calculus appl…
In some previous papers, a Legendre duality between Lagrangian and Hamiltonian Mechanics has been developed. The (ρ,η)-tangent application of the Legendre bundle morphism associated to a Lagrangian L or Hamiltonian H is presented. Using that, a Legendre description of Lagrangian Mechanics and Hamiltonian Mechanics is d…
Paper bridges quantum and classical mechanics for open systems.
Paper presents a new approach to continuum mechanics using port-Hamiltonian framework.
Proposes NSSNNs to predict nonseparable Hamiltonian systems.
Differentiable simulations control molecular Hamiltonians for desired outcomes.
Generalizes momentum map to Courant algebroid for constrained mechanics.
The constraint reaction force of ideal nonholonomic constraints in time-dependent mechanics on a configuration bundle is obtained. Using the vertical extension of Hamiltonian formalism to the vertical tangent bundle of , the Hamiltonian of a nonholonomic constrained system is constructed.
We develop a new geometric framework suitable for dealing with Hamiltonian field theories with dissipation. To this end we define the notions of -contact structure and -contact Hamiltonian system. This is a generalization of both the contact Hamiltonian systems in mechanics and the -symplectic Hamiltonian syst…
Generalizes energy-momentum method for non-autonomous Hamiltonian systems.
Gaussian process model learns Hamiltonian systems from noisy data.
Geometrically reduces Hamiltonian systems using particular integrals.
Geometrically transforms nonconservative dynamics to linearize Kepler and Manev systems.
A general, consistent and complete framework for geometrical formulation of mechanical systems is proposed, based on certain structures on affine bundles (affgebroids) that generalize Lie algebras and Lie algebroids. This scheme covers and unifies various geometrical approaches to mechanics in the Lagrangian and Hamilt…
Develops integrators for contact Hamiltonian systems preserving geometric structure.
In this paper we show that the Hamiltonian Monte Carlo method for compact Lie groups constructed in \cite{kennedy88b} using a symplectic structure can be recovered from canonical geometric mechanics with a bi-invariant metric. Hence we obtain the correspondence between the various formulations of Hamiltonian mechanics …
Alternative discrete Dirac mechanics using Dirac structures.
A new Dirac algebroid approach for nonholonomic systems.
In this study, we introduce Euler-Lagrange and Hamiltonian equations on (R2; g; J) being a model of para-Kaehlerian Space Forms. Finally, some geometrical and physical results on the related mechanic systems have been discussed.
We show a constrained Hamiltonian system and a gauged sigma model have a structure of a momentum section and a Hamiltonian Lie algebroid theory recently introduced by Blohmann and Weinstein. We propose a generalization of a momentum section on a pre-multisymplectic manifold by considering gauged sigma models on a highe…
We introduce and study the basic notion of polarized Poisson manifolds generalizing the classical case of Poisson manifolds and extend this last notion for the % symplectic stuctures. And also, we show that for any polarized Hamiltonian map, the associated Nambu's dynamical system and polarized Hamiltonian system…
Develops integrators for Hamiltonian systems in Jacobi manifolds.
Newtonian, Lagrangian, and Hamiltonian dynamical systems are well formalized mathematically. They give rise to geometric structures describing motion of a point in smooth manifolds. Riemannian metric is a different geometric structure formalizing concepts of length and angle. The interplay of Riemannian metric and its …
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. Building on previous work on the Hamiltonian theory of impact, we tackle the prob…
Paper analyzes dynamics of nonholonomic systems with collisions using variational techniques.
The aim of this paper is to study the relationship between Hamiltonian dynamics and constrained variational calculus. We describe both using the notion of Lagrangian submanifolds of convenient symplectic manifolds and using the so-called Tulczyjew's triples. The results are also extended to the case of discrete dynamic…
In this paper, we describe a constrained Lagrangian and Hamiltonian formalism for the optimal control of nonholonomic mechanical systems. In particular, we aim to minimize a cost functional, given initial and final conditions where the controlled dynamics is given by nonholonomic mechanical system. In our paper, the co…
In this paper, we consider a generalization of variational calculus which allows us to consider in the same framework different cases of mechanical systems, for instance, Lagrangian mechanics, Hamiltonian mechanics, systems subjected to constraints, optimal control theory and so on. This generalized variational calculu…
The paper adapts results for Reeb flows and Hamiltonian flows, showing all orbits are closed have identical periods.
Study symmetry breaking in quantum mechanics to understand many-body physics.
The Rusk-Skinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems. It incorporates all the characteristics of Lagrangian and Hamiltonian descriptions of these systems (including dynamical equations and solutions, constraints, Legendre map, evolution operators, e…
We discuss the quantization of mechanical systems for which the Hamiltonian vector fields of observables form the deformation of -dimensional oscilator algebra. Because of this fact these systems can be considered as "deformations" of the harmonic oscillator. The set of abovementioned mechanical systems are realized…
Invariant reduction preserves Poisson structures in PDEs.
An example of mechanical system whose configuration space is direct product of a curved space and the local group of rotations, is presented. The system is considered as a model of spinning particle moving in the space. The Hamiltonian formalism for this system and possible method for its quantization are discussed. It…
The curvature and the reduced curvature are basic differential invariants of the pair (Hamiltonian system, Lagrange distribution) on the symplectic manifold. It is shown that the negativity of the reduced curvature implies the hyperbolicity of any compact invariant set of the Hamiltonian flow restricted to a prescribed…
SGNs use Hamiltonian mechanics for invertible deep generative modeling.
We are able to derive the equations of motion for forced mechanical systems in a purely variational setting, both in the context of Lagrangian or Hamiltonian mechanics, by duplicating the variables of the system as introduced by Galley [2013], Galley, Tsang, and Stein [2014]. We show that this construction is useful to…
The purpose of this paper is to describe geometrically discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids. From a variational principle we derive the discrete Euler-Lagrange equations and we introduce a symplectic 2-section, which is preserved by the Lagrange evolution operator. In terms of the discrete Leg…
Reduces equations for contact mechanical systems on Lie groups by exploiting symmetries.