A drift-free left invariant control system on the Lie group \(\mathrm{SO}(3) \times \mathbb R^3 \times \mathbb R^3\)
type: Item
instance of: scholarly article
title: A drift-free left invariant control system on the Lie group \(\mathrm{SO}(3) \times \mathbb R^3 \times \mathbb R^3\)
zbMATH Open document ID: 1394.70046
DOI: 10.1155/2015/652819
author: Y. Aharonov
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: A controllable drift-free system on the Lie group \(G = \mathrm{SO}(3) \times \mathbb R^3 \times \mathbb R^3\) is considered. The dynamics and geometrical properties of the corresponding reduced Hamilton's equations on \(\left(g^{ast}, \left\{\cdot, \cdot\right\}_-\right)\) are studied, where \(\left\{\cdot, \cdot\right\}_-\) is the minus Lie-Poisson structure on the dual space \(g^{\ast}\) of the Lie algebra \(g = so(3) \times \mathbb R^3 \times \mathbb R^3\) of \(G\). The numerical integration of this system is also discussed.
Mathematics Subject Classification ID: 70G45
Mathematics Subject Classification ID: 93B05
zbMATH DE Number: 6926920
Wikidata QID: Q59119330
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/652819
OpenAlex ID: W1540694487
cites work: The geometry of the plate-ball problem
cites work: Some new remarks about the dynamics of an automobile with two trailers
cites work: Multiple Lie-Poisson structures, reductions, and geometric phases for the Maxwell-Bloch travelling wave equations
cites work: An optimal control problem on the Lie group \(SE(2,\mathbb{R})\times SO(2)\)
cites work: Stability of a bottom-heavy underwater vehicle
cites work: Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung
cites work: Simple evaluation of Casimir invariants in finite-dimensional Poisson systems
cites work: Q5516802
cites work: On the Product of Semi-Groups of Operators
cites work: Controllability problems in the charged top dynamics
cites work: Cost-extended control systems on Lie groups
cites work: AN OPTIMAL CONTROL PROBLEM ON THE LIE GROUP SO(4)
cites work: ON A HAMILTONIAN VERSION OF CONTROLS DYNAMIC FOR A DRIFT-FREE LEFT INVARIANT CONTROL SYSTEM ON G4
cites work: Control theory from the geometric viewpoint.
cites work: Q4067388
description: scientific article; zbMATH DE number 6926920