The Moser-Veselov equation
type: Item
instance of: scholarly article
title: The Moser-Veselov equation
zbMATH Open document ID: 1020.15016
DOI: 10.1016/S0024-3795(02)00450-0
published in: Linear Algebra and its Applications
publication date: 2003-03-11T00:00:00Z
review text: The orthogonal solutions of the matrix equation \[ XJ-JX^{T}=M\tag{1} \] are studied, where \(J\) is symmetric positive definite and \(M\) is skew-symmetric. This Moser-Veselov equation is the discrete version of the Euler-Arnold equation for the motion of the generalized rigid body. It is shown that every orthogonal solution of (1) can be written in the form \(X=(M/2+S)J^{-1}\), where \(S\) is a symmetric solution of the algebraic Riccati equation \[ S^{2}+S(M/2)+(M/2)^{T}S-(M^{2}/4+J^{2})=0. \] By using the Riccati equations theory, existence and uniqueness theorems are obtained for equation (1) and an algorithm for determining a special orthogonal solution is given. Explicit formulae for the solutions of (1) are obtained in the particular case \(J=I\). This case is associated with the continuous version of the dynamics of a rigid body.
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 70E15
Mathematics Subject Classification ID: 93B60
zbMATH DE Number: 1880039
zbMATH Keywords: algebraic Riccati equation
zbMATH Keywords: controllability
zbMATH Keywords: stability
zbMATH Keywords: primary matrix functions
zbMATH Keywords: orthogonal solutions
zbMATH Keywords: Moser-Veselov equation
zbMATH Keywords: Euler-Arnold equation
zbMATH Keywords: algorithm
zbMATH Keywords: dynamics of a rigid body
author: João R. Cardoso
author: Fátima Silva Leite
reviewed by: Valeriu Prepeliţă
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1880039