Results 221 to 230 of about 235,971 (249)

Paths in sub-Riemannian geometry

2007
In sub-Riemannian geometry only horizontal paths — i.e. tangent to the distribution — can have finite length. The aim of this talk is to study non-horizontal paths, in particular to measure them and give their metric dimension. For that we introduce two metric invariants, the entropy and the complexity, and corresponding measures of the paths depending
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Curvature in sub-Riemannian geometry

Journal of Mathematical Physics, 2012
We study curvature problems on a nearly Riemannian manifold, which is a sub-Riemannian manifold (M, HM, g, VM) whose adapted tensor field given by (2.2) vanishes identically. First, we prove the existence and uniqueness of what we call horizontal Riemannian connection, which is a torsion-free and metric linear connection ∇ on the horizontal ...
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Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics

, 2017
This is a survey of the main forms of equations of dynamical systems with non-integrable constraints, divided into two large groups. The first group contains systems arising in vakonomic mechanics and optimal control theory, with the equations of motion ...
A. Borisov, I. Mamaev, I. Bizyaev
semanticscholar   +1 more source

Numerical methods for sub-Riemannian geometry [PDF]

Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), 2003
Consider a sub-Riemannian geometry (U,/spl Delta/,g) where U is a neighborhood of 0 in R/sup n/, /spl Delta//spl sub/TR/sup n/ a distribution of constant rank m and g a Riemannian metric defined on /spl Delta/. One of the main questions related to a given sub-Riemannian structure is the description of the conjugate and cut loci, of the sphere and the ...
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Foucault pendulum and sub-Riemannian geometry

Journal of Mathematical Physics, 2010
The well known Foucault nonsymmetrical pendulum is studied as a problem of sub-Riemannian geometry on nilpotent Lie groups. It is shown that in a rotating frame a sub-Riemannian structure can be naturally introduced. For small oscillations, three dimensional horizontal trajectories are computed and displayed in detail.
A. Anzaldo-Meneses, F. Monroy-Pérez
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Measures of transverse paths in sub-Riemannian geometry

Journal d'Analyse Mathématique, 2003
We define a class of lengths of paths in a sub-Riemannian manifold. It includes the length of horizontal paths but also measures the length of transverse paths. It is obtained by integrating an infinitesimal measure which generalizes the norm on the tangent space. This requires the definition and the study of the metric tangent space (in Gromov's sense)
Falbel, Elisha, Jean, Frédéric
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Sub-Riemannian geometry and nonholonomic mechanics

AIP Conference Proceedings, 2011
The purpose of the present paper is to study the geometry of a sub‐Riemannian manifold and to apply the results to the nonholonomic mechanical systems. First, we construct a linear connection on the horizontal distribution and obtain some Bianchi identities for it.
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Sub-Riemannian Geometry and Hypoelliptic Operators

2017
In this course we carefully define the notion of a non-holonomic manifold, which is a manifold with a certain non-integrable smooth sub-bundle of the tangent bundle, also called a distribution. We define such concepts as horizontal distributions, bracket generating condition for distributions, a sub-Riemannian structure, hypoelliptic and subelliptic ...
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Sub-Riemannian Geometry and Subelliptic PDEs

2003
Ishall discuss the connection between complex Hamiltonian mechanics and sub-Riemannian geometry on the Heisenberg group. Using these geometric concepts I shall describe the subelliptic heat kernel and its small time asymptotics. To extend this work to higher step operators I shall apply some of these concepts to a particular step 3 example.
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Programmable interactions and emergent geometry in an array of atom clouds

Nature, 2021
Avikar Periwal, Julian F Wienand, Eric S Cooper   +2 more
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