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A Journal of Russian Academy of Sciences
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IssuesArchive of Issues2021-6pp.996-1003

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Murashkin E.V. and Radayev Yu.N., "Generalization of the Algebraic Hamilton-Cayley Theory," Mech. Solids. 56 (6), 996-1003 (2021)
Year 2021 Volume 56 Number 6 Pages 996-1003
DOI 10.3103/S0025654421060145
Title Generalization of the Algebraic Hamilton-Cayley Theory
Author(s) Murashkin E.V. (Ishlinskii Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526 Russia, evmurashkin@gmail.com)
Radayev Yu.N. (Ishlinskii Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526 Russia, y.radayev@gmail.com)
Abstract The paper presents generalizations of the vector and mixed product concepts including indication of their connection with the fundamental orienting pseudoscalar, necessary for constructing the algebraic Hamilton-Cayley theory for space of arbitrary given dimension n in the pseudotensor case. In existing studies dealing with the mechanics of solids, the case of three-dimensional space is usually considered. The proof of the Hamilton-Cayley theorem is carried out in a pseudotensor formulation. The weight of the pseudotensor is assumed to be an integer. The given examples are tensors of the micropolar theory of elasticity, in particular, hemitropic micropolar elasticity. The dynamic equations for the hemitropic micropolar continuum are discussed in terms of pseudotensors.
Keywords pseudotensor, pseudo-affinor, fundamental orienting pseudoscalar, skew product, invariant, comitant, micropolar hemitropic continuum
Received 21 April 2021Revised 24 April 2021Accepted 26 April 2021
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