The Tensor Equation AX+XA=Phi (A, H) with Applications to Kinematics of Continua

Abstract

The (secon-order) tensor equation AX + XA = Phi (A,H) is studied for certain isotropic functions Phi (A,H) which are linear in H. Qualitative properties of the solution X and relations between the solutions for forms of Phi are established for an inner product space of arbitrary dimension. These results, together with Rivlin's identities for tensor polynomials in two variables, are applied in three dimension to obtain new explicit formulas for X in direct tensor notation as well as new derivations of previously known formulas. Several applications to the kinematics of continua are considered. Kinematics, Matrix equations, Tensors

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1994
Accession Number
ADA285886

Entities

People

  • Michael J. Scheidler

Organizations

  • United States Army Research Laboratory

Tags

Communities of Interest

  • Energy and Power Technologies
  • Weapons Technologies

DTIC Thesaurus Topics

  • Coefficients
  • Continuum Mechanics
  • Decomposition
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Kinematics
  • Linear Algebraic Equations
  • Materials
  • Mechanics
  • Military Research
  • Polynomials
  • Theorems
  • Three Dimensional
  • Two Dimensional
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Linear Algebra
  • Mechanical Engineering/Mechanics of Materials.

Technology Areas

  • Space