Summary
In this work we develop a frame-independent approach to the notion of convected derivation, and give a systematic classification of these derivatives in terms of an absolute vorticity and deformation rate in classical space-time. In the case of derivatives following a motion we distinguish between intrinsic and extrinsic convected derivatives. A link is established between the class of convected derivatives and the class of affine connections on classical space-time compatible with its metric structure.
Riassunto
In questo lavoro si sviluppa un approccio indipendente dalla struttura alla nozione di derivazione di convezione e di dà una classificazione sistematica di queste derivate nei termini di un assoluto rapporto di deformazione e vorticità nello spazio-tempo classico. Nel caso di derivate che seguono un moto si distingue tra derivate di convezione intrinseche ed estrinseche. Si determina un legame tra la classe di connessioni di convezione e la classe di connessioni affini sullo spazio-tempo classico compatibile con la sua struttura metrica.
резюме
В этой работе мы развиваем не зависящий от системы отсчета подход к определению конвективной производной и проводим систематическую классификацию этих производных в терминах абсолютной завихренности и интенсивности деформации в классическом пространстве-времени. В случае производных, определяющих движение, мы различаем собственные и несобственные конвективные производные. Устанавливается связь между классом конвективных производных и классом аффинных связей на классическом пространстве-времени, совместимом с метрической структурой.
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Appleby, P.G., Kadianakis, N. Convected time derivatives in continuum mechanics. Nuov Cim B 102, 593–608 (1988). https://doi.org/10.1007/BF02725618
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DOI: https://doi.org/10.1007/BF02725618