Zobrazeno 1 - 10
of 278
pro vyhledávání: '"37J60"'
Autor:
Peng, Linyu, Yoshimura, Hiroaki
In this paper, we propose the concept of $(\pm)$-discrete Dirac structures over a manifold, where we define $(\pm)$-discrete two-forms on the manifold and incorporate discrete constraints using $(\pm)$-finite difference maps. Specifically, we develop
Externí odkaz:
http://arxiv.org/abs/2411.09530
In this paper, we prove that the trajectories of unreduced $\phi$-simple Chaplygin kinetic systems are reparametrizations of horizontal geodesics with respect to a modified Riemannian metric. Furthermore, our proof is constructive and these Riemannia
Externí odkaz:
http://arxiv.org/abs/2409.18648
We introduce a class of examples which provide an affine generalization of the nonholonomic problem of a convex body rolling without slipping on the plane. We investigate dynamical aspects of the system such as existence of first integrals, smooth in
Externí odkaz:
http://arxiv.org/abs/2409.08072
Autor:
Jovanovic, Bozidar
We study the relativistic formulation of a classical time-dependent nonholonomic Lagrangian mechanics from the perspective of moving frames. We also introduce time-dependent $G$-Chaplygin systems with affine constraints, which are natural objects for
Externí odkaz:
http://arxiv.org/abs/2407.06231
Autor:
Kilin, Alexander, Pivovarova, Elena
This paper is concerned with the problem of an ellipsoid of revolution rolling on a horizontal plane under the assumption that there is no slipping at the point of contact and no spinning about the vertical. A reduction of the equations of motion to
Externí odkaz:
http://arxiv.org/abs/2405.07511
We present some rigorous results on the absence of a wide class of invariant measures for dynamical systems possessing attractors. We then consider a generalization of the classical nonholonomic Suslov problem which shows how previous investigations
Externí odkaz:
http://arxiv.org/abs/2404.14156
Autor:
Belrhazi, Malika, Mestdag, Tom
For a Lagrangian system with nonholonomic constraints, we construct extensions of the equations of motion to sets of second-order ordinary differential equations. In the case of a purely kinetic Lagrangian, we investigate the conditions under which t
Externí odkaz:
http://arxiv.org/abs/2404.11997
Autor:
De León, Manuel, Jiménez, Víctor M.
In this paper we study contact nonholonomic mechanical sys\-tems. We construct a general framework for non-holonomic constraints in contact geometry and, in this framework, we define different nonholonomic brackets using con\-venient \linebreak decom
Externí odkaz:
http://arxiv.org/abs/2312.15044
Autor:
Basalaev, Sergey, Agapov, Sergei
Publikováno v:
Anal.Math.Phys. 14, 58 (2024)
We study the nonholonomic motion of a point particle on the Heisenberg group around the fixed "sun" whose potential is given by the fundamental solution of the sub-Laplacian. Unlike arXiv:1212.2713 where the variational problem is studied we consider
Externí odkaz:
http://arxiv.org/abs/2311.15746
We discuss the rolling, without slip and without twist, of Stiefel manifolds equipped with $\alpha$-metrics, from an intrinsic and an extrinsic point of view. We, however, start with a more general perspective, namely by investigating intrinsic rolli
Externí odkaz:
http://arxiv.org/abs/2309.14854