The Tensor Equation AX + XA = G

Abstract

We study the second-order tensor equation AX + XA = G for symmetric, positive-definite A and arbitrary G. Motivated by applications in the continuum mechanics literature, we also examine some special cases where G depends on A and another tensor H. For arbitrary dimensions, we establish relations between the solutions X for various forms of G. These results, together with Rivlin's identities for tensor polynomials in two variables, are applied in two and three dimensions to obtain explicit formulas for X in direct (component-free) notation. The results include new formulas as well as new derivations of previously known formulas. An application to the kinematics of rigid motions is considered.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1992
Accession Number
ADA246665

Entities

People

  • Mike Scheidler

Organizations

  • Ballistic Research Laboratory

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Army
  • Artillery
  • Commerce
  • Continuum Mechanics
  • Eigenvalues
  • Elastic Properties
  • Engineering
  • Equations
  • Identities
  • Materials
  • Mechanics
  • Notation
  • Polynomials
  • Three Dimensional
  • Two Dimensional
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Linear Algebra