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On the interrelation of the basic laws of continuum mechanics
Author(s) -
Kienzler Reinhold,
Herrmann George
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310366
Subject(s) - conservation law , continuum mechanics , balance (ability) , classical mechanics , theory of relativity , foundation (evidence) , invariant (physics) , analytical mechanics , mathematics , theoretical physics , physics , mechanics , law , mathematical analysis , mathematical physics , political science , psychology , quantum mechanics , neuroscience , quantum dynamics , quantum
It has been shown by the present authors in a recent paper [1] that if some conservation and balance laws of continuum mechanics are represented in a 4 × 4 form, balance of linear physical momentum (i. e., stress) and balance of mass become closely linked. This seemingly novel result was reached in a completely ad‐hoc fashion by treating time on the same level as the spatial coordinates, and not as parameter, as it is usually done. In order to place the above ad‐hoc result on a firmer foundation and since it is in the theory of relativity that space and time are considered on the same footing, an attempt is made to derive several tensors of continuum mechanics in a systematic manner as 4 × 4 invariant objects.