相关论文: A relativistic generalisation of rigid motions

Fermat-holonomic congruences are proposed as a weaker substitute for the too restrictive class of Born-rigid motions. The definition is expressed as a set of differential equations. Integrability conditions and Cauchy data are studied.

Causal rigid particles whose action includes an {\it arbitrary} dependence on the world-line extrinsic curvature are considered. General classes of solutions are constructed, including {\it causal tachyonic} ones. The Hamiltonian…

The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…

A 2-dimensional point-line framework is a collection of points and lines in the plane which are linked by pairwise constraints that fix some angles between pairs of lines and also some point-line and point-point distances. It is rigid if…

Lagrangian systems with nonholonomic constraints may be considered as singular differential equations defined by some constraints and some multipliers. The geometry, solutions, symmetries and constants of motion of such equations are…

Nonholonomic systems are variational models commonly used for mechanical systems with ideal no-slip constraints. This note provides a differential-geometric derivation of the nonholonomic equations of motion for an arbitrary rigid body…

The aim of this paper is to perform a deeper geometric analysis of problems appearing in dynamics of affinely rigid bodies. First of all we present a geometric interpretation of the polar and two-polar decomposition of affine motion. Later…

The group of rigid motions is considered to guide the search for a natural system of space-time coordinates in General Relativity. This search leads us to a natural extension of the space-times that support Painlev\'{e}--Gullstrand…

We establish elliptic regularity for nonlinear inhomogeneous Cauchy-Riemann equations under minimal assumptions, and give a counterexample in a borderline case. In some cases where the inhomogeneous term has a separable factorization, the…

This paper is devoted to the comparison of the notions of regularity for algebraic connections and (holonomic) regularity for algebraic $\mathcal D$-modules.

A new approach to relativistic mechanics is proposed, suitable to describe dynamics of different kinds of relativistic particles. Mathematically it is based on an application of the recent geometric theory of nonholonomic systems on fibred…

This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…

We define and study slider-pinning rigidity, giving a complete combinatorial characterization. This is done via direction-slider networks, which are a generalization of Whiteley's direction networks.

We develop the theory of relative regular holonomic D-modules with a smooth complex manifold S of arbitrary dimension as parameter space, together with their main functorial properties. In particular, we establish in this general setting…

We study the possibility that galactic rotation curves can be explained by a gravitational potential that contains a linear term as well as a Newtonian one. This hypothesis, suggested by conformal gravity, does allow good fits to the…

Canonical formalism for SO(2) is developed. This group can be seen as a toy model of the Hamilton-Dirac mechanics with constraints. The Lagrangian and Hamiltonian are explicitly constructed and their physical interpretation are given. The…

We develop a holonomy reduction procedure for general Cartan geometries. We show that, given a reduction of holonomy, the underlying manifold naturally decomposes into a disjoint union of initial submanifolds. Each such submanifold…

An important, if relatively less well known aspect of the singularity theorems in Lorentzian Geometry is to understand how their conclusions fare upon weakening or suppression of one or more of their hypotheses. Then, theorems with modified…

We give an argument that a broad class of geometric models of spinning relativistic particles with Casimir mass and spin being separately fixed parameters, have indeterminate worldline (while other spinning particles have definite…

We consider spaces for which there is a notion of harmonicity for complex valued functions defined on them. For instance, this is the case of Riemannian manifolds on one hand, and (metric) graphs on the other hand. We observe that it is…