A software package for Lie algebraic computations
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Date
2005
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Publisher
SIAM PUBLICATIONS
Abstract
The paper presents a computer algebra package that facilitates Lie algebraic symbolic computations required in the solution of a variety of problems, such as the solution of right-invariant differential equations evolving on Lie groups. Lie theory is a powerful tool, helpful in the analysis and design of modern nonlinear control laws, nonlinear filters, and the study of particle dynamics. The practical application of Lie theory often results in highly complex symbolic expressions that are difficult to handle efficiently without the aid of a computer software tool. The aim of the package is to facilitate and encourage further research relying on Lie algebraic computations.
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Keywords
Lie algebras, Lie groups, Campbell-Baker-Hausdorff formula, Hall bases, Wei-Norman equations, symbolic computation, computer algebra, differential equations, control systems, nonlinear filtering, DIFFERENTIAL-EQUATIONS, SUFFICIENT CONDITION, SYMMETRIES, SYSTEMS, CONTROLLABILITY, STABILIZATION, COMBINATORICS, FORMULA, POINT