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.
This paper studies nonholonomic constraints in Hamiltonian systems, deriving equations and theorems.
Exact discrete mechanics for nonholonomic systems defined.
Study nonholonomic systems with collisions using variational principles.
In this paper, for a variety of nonholonomic (reducible) Hamiltonian systems, we first give to various distributional Hamiltonian systems, by analyzing carefully the dynamics and structures of the nonholonomic Hamiltonian systems. Secondly, we derive precisely the geometric constraint conditions of the induced distribu…
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 conditions that guarantee that the dynamics of the system can be obtained as a suitabl…
Paper analyzes dynamics of nonholonomic systems with collisions using variational techniques.
Geodesic extensions for systems with nonholonomic constraints.
The reduction of nonholonomic systems is formulated in terms of Dirac reduction. An optimal reduction method for a class of nonholonomic systems is formulated. Several examples are studied in detail.
Generalizes Newmark methods for nonholonomic systems.
This paper studies Hamilton-Jacobi equations for magnetic systems with constraints.
In this article we develop a theory of contact systems with nonholonomic constraints. We obtain the dynamics from Herglotz's variational principle, by restricting the variations so that they satisfy the nonholonomic constraints. We prove that the nonholonomic dynamics can be obtained as a projection of the unconstraine…
This paper studies the construction of geometric integrators for nonholonomic systems. We derive the nonholonomic discrete Euler-Lagrange equations in a setting which permits to deduce geometric integrators for continuous nonholonomic systems (reduced or not). The formalism is given in terms of Lie groupoids, specifyin…
Paper extends Noether's Theorem to nonholonomic systems, proving conserved momentum.
Paper reduces nonholonomic systems with symmetries.
Paper introduces Eden bracket for nonholonomic systems.
The paper explores infinite-dimensional nonholonomic and vakonomic systems.
New proof shows nonholonomic motions are geodesics, minimizing distance.
This paper deals with conservation laws for mechanical systems with nonholonomic constraints. It uses a Lagrangian formulation of nonholonomic systems and a Cartan form approach. We present what we believe to be the most general relations between symmetries and first integrals. We discuss the so-called nonholonomic Noe…
Study on relativistic nonholonomic mechanics with time-dependent constraints.
Projective geodesic extensions for nonholonomic systems are derived under conformal transformations.
Defines Jacobi fields in nonholonomic mechanics.
This work extends reduction processes for nonholonomic discrete mechanical systems.
This paper simplifies complex nonholonomic systems using momentum map reduction.
The paper compares numerical schemes for nonholonomic systems using retraction maps.
Develops integrators for nonholonomic systems on Lie groups.
We study the tracking of a trajectory for a nonholonomic system by recasting the problem as a constrained optimal control problem. The cost function is chosen to minimize the error in positions and velocities between the trajectory of a nonholonomic system and the desired reference trajectory, both evolving on the dist…
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 systems subject to nonholonomic constraints and that are invariant under the ac…
Study on friction forces for nonholonomic systems using affine connections.
The paper defines and proves equivalence of nonholonomic brackets in contact mechanical systems.
Study magnetic Hamiltonian systems with constraints, deriving Hamilton-Jacobi equations.
In this paper, we propose a geometric integrator for nonholonomic mechanical systems. It can be applied to discrete Lagrangian systems specified through a discrete Lagrangian defined on QxQ, where Q is the configuration manifold, and a (generally nonintegrable) distribution in TQ. In the proposed method, a discretizati…
This paper presents a geometric description on Lie algebroids of Lagrangian systems subject to nonholonomic constraints. The Lie algebroid framework provides a natural generalization of classical tangent bundle geometry. We define the notion of nonholonomically constrained system, and characterize regularity conditions…
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.
A new Dirac algebroid approach for nonholonomic systems.
New integrators for Lagrangian systems on homogeneous spaces derived from nonholonomic 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 bracket gives rise to a new bracket on the reduced space codifying the nonholonomic …
Study on nonholonomic mechanics and sub-Finsler geometry.
New bracket unifies nonholonomic dynamics and Hamilton-Jacobi theory.
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…
We address the problem of constructing numerical integrators for nonholonomic Lagrangian systems that enjoy appropriate discrete versions of the geometric properties of the continuous flow, including the preservation of energy. Building on previous work on time-dependent discrete mechanics, our approach is based on a d…
In this paper we propose a process of lagrangian reduction and reconstruction for nonholonomic discrete mechanical systems where the action of a continuous symmetry group makes the configuration space a principal bundle. The result of the reduction process is a discrete dynamical system that we call the discrete reduce…
New bracket theory connects three nonholonomic dynamics models.
Geometrically characterizes virtual nonlinear nonholonomic constraints using symplectic methods.
This is the second paper in a series of works devoted to nonholonomic Ricci flows. By imposing non-integrable (nonholonomic) constraints on the Ricci flows of Riemannian metrics we can model mutual transforms of generalized Finsler-Lagrange and Riemann geometries. We verify some assertions made in the first partner pap…
Survey of recent developments in symmetric reductions and controls for Hamiltonian systems.
In this paper, we explore dynamics of the nonholonomic system called vakonomic mechanics in the context of Lagrange-Dirac dynamical systems using a Dirac structure and its associated Hamilton-Pontryagin variational principle. We first show the link between vakonomic mechanics and nonholonomic mechanics from the viewpoi…
In the present article the geometry of semi-Riemannian manifolds with nonholonomic constraints is studied. These manifolds can be considered as analogues to the sub-Riemannian manifolds, where the positively definite metric is substituted by a nondegenerate metric. To study properties of the exponential map the Christo…
Survey of Lagrangian reduction for discrete mechanical systems.