Powered by OpenAIRE graph
Found an issue? Give us feedback
addClaim

Rolling motions of pseudo-orthogonal groups

Authors: Peter E. Crouch; Fatima Silva Leite;

Rolling motions of pseudo-orthogonal groups

Abstract

The classical definition of a rolling map, describing the rolling motion, without slip or twist, of one Euclidean submanifold over another of the same dimension, as given in Sharpe [8], is generalized for the situation when the embedded space is equipped with a pseudo-Riemannian metric and applied to derive the kinematic equations for the constrained rolling motion of a connected pseudo-Riemannian orthogonal group over its affine tangent spaces at a point. The kinematic equations are solved explicitly when the curve along which the first manifold rolls is a geodesic. We also show that rolling motions along a curve with non-holonomic constraints of not-wist and no-slip encode parallel transport, and derive formulas for the tangent and normal parallel transport of a vector along geodesics. Finally, we make a brief reference on how rolling motions can be used to generate smooth interpolating curves on pseudo-orthogonal groups.

Related Organizations
  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    6
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
6
Top 10%
Average
Average
Upload OA version
Are you the author of this publication? Upload your Open Access version to Zenodo!
It’s fast and easy, just two clicks!