Connections on the path bundle of a principal fiber bundle

The Principal Fiber Bundle Structure of the Gimbal-Spacecraft System

Nomenclature β,γ(∈ S) = The gimbal and wheel angles. (rad) Rβ(∈ SO(3)) = Transformation from gimbal frame G to the spacecraft body frame B. Is = Spacecraft inertia without the CMG gimbal and wheel inertia. (kg.m) Ig, Ir = Gimbal frame inertia, wheel inertia about own centre of mass represented in gimbal frame. (kg.m) (Igr)β = Combined inertia of gimbal frame and wheel in the spacecraft frame. R...

holonomy of connections over a bundle map

In this paper we introduce a generalisation of the notion of holonomy for connections over a bundle map on a principal fibre bundle. We prove that, as in the standard theory on principal connections, the holonomy groups are Lie subgroups of the structure group of the principle fibre bundle and we also derive a straightforward generalisation of the Reduction Theorem.

0 Fe b 20 07 CONNECTIONS ON A PARABOLIC PRINCIPAL BUNDLE , II

In [Bi2] we defined connections on a parabolic principal bundle. While connections on usual principal bundles are defined as splittings of the Atiyah exact sequence, it was noted in [Bi2] that the Atiyah exact sequence does not generalize to the parabolic principal bundles. Here we show that a twisted version of the Atiyah exact sequence generalize to the context of parabolic principal bundles....

Choosing the Best Bundle of Projects: A DEA Approach

The Lie Algebra of Smooth Sections of a T-bundle

In this article, we generalize the concept of the Lie algebra of vector fields to the set of smooth sections of a T-bundle which is by definition a canonical generalization of the concept of a tangent bundle. We define a Lie bracket multiplication on this set so that it becomes a Lie algebra. In the particular case of tangent bundles this Lie algebra coincides with the Lie algebra of vector fie...