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GENERALIZATION OF THE ALGEBRAIC HAMILTON–CAYLEY THEORY

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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.

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Notes

  1. In fact, when deriving the Hamilton–Cayley equation, we did not use the concept of the Euclidean metric of the space, which means the validity of equation (3.14) in the case of an arbitrary n-dimensional space

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Funding

The study was carried out within the framework of a state assignment (state registration no. АААА-А20-120011690132-4) and with the support of the Russian Foundation for Basic Research projects no. 19-51-60001, no. 20-01-00666.

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  1. Ishlinskii Institute for Problems in Mechanics, Russian Academy of Sciences, 119526, Moscow, Russia

    E. V. Murashkin & Yu. N. Radayev

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  1. E. V. Murashkin
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  2. Yu. N. Radayev
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Correspondence to E. V. Murashkin or Yu. N. Radayev.

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Translated by A.A. Borimova

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Murashkin, E.V., Radayev, Y.N. GENERALIZATION OF THE ALGEBRAIC HAMILTON–CAYLEY THEORY. Mech. Solids 56, 996–1003 (2021). https://doi.org/10.3103/S0025654421060145

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  • DOI: https://doi.org/10.3103/S0025654421060145

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