Twirl tensors and the tensor equation \(AX-XA=C\)

DOI10.1007/BF00041688zbMath0757.15021OpenAlexW2071687683MaRDI QIDQ1198443

Haoyun Liang, Zhongheng Guo, Th. Lehmann, Chi-Sing Man

Publication date: 16 January 1993

Published in: Journal of Elasticity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00041688

zbMATH Keywords

stress tensorspectral decompositioninertia tensortensor equationsecond-order symmetric tensortwirl tensor

Mathematics Subject Classification ID

Vector and tensor algebra, theory of invariants (15A72) Matrix equations and identities (15A24) Eigenvalues, singular values, and eigenvectors (15A18)

Related Items (12)

Some basis-free expressions for stresses conjugate to Hill's strains through solving the tensor equation \(AX + XA = C\) ⋮ The explicit solution of the matrix equation \(AX-XB = C\) ⋮ Principal axis intrinsic method and the high dimensional tensor equation \(AX-XA=C^*\) ⋮ The linear bi-spatial tensor equation \(\varphi_{ij}A^iXB^j=C\) ⋮ Coordinate-independent representation of spins in continuum mechanics ⋮ Families of continuous spin tensors and applications in continuum mechanics ⋮ Some basis-free formulae for the time rate and conjugate stress of logarithmic strain tensor ⋮ Basis-free expressions for families of objective strain tensors, their rates, and conjugate stress tensors ⋮ On the objective corotational rates of Eulerian strain measures ⋮ New results for the spin of the Eulerian triad and the logarithmic spin and rate ⋮ The Derivative of Isotropic Tensor Functions, Elastic Moduli and Stress Rate: I. Eigenvalue Formulation ⋮ Derivatives on the isotropic tensor functions

Cites Work

• Spin and rotation velocity of the stretching frame in continuum mechanics
• On the operator equation \(BX - XA = Q\)
• The material time derivative of logarithmic strain
• A Finite Series Solution of the Matrix Equation $AX - XB = C$
• Matrix Equation $XA + BX = C$
• Solution of the Equation $AX + XB = C$ by Inversion of an $M \times M$ or $N \times N$ Matrix
• Solution of the Matrix Equations $AX + XB = - Q$ and $S^T X + XS = - Q$
• Explicit Solutions of Linear Matrix Equations
• The Equations AX - YB = C and AX - XB = C in Matrices
• Unnamed Item

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