Sat, 26 Jul 2008 07:53:35 BST CiteULike: norris's relativity http://www.citeulike.org/user/norris/tag/relativity CiteULike.org en-gb Copyright © 2004-2008 citeulike.org http://www.citeulike.org/user/norris/article/1829667 <i>PAMM, Vol. 3, No. 1. (2003), pp. 182-185.</i><br /><br />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. On the interrelation of the basic laws of continuum mechanics Reinhold Kienzler George Herrmann doi:10.1002/pamm.200310366 PAMM, Vol. 3, No. 1. (2003), pp. 182-185. 2007-10-27T17:10:11-00:00 2003 PAMM 3 1 182 185 relativity http://www.citeulike.org/user/norris/article/1829657 <i>pp. 145-150.</i> On the representation of basic laws of continuum mechanics by 4 x 4 tensors G Herrmann pp. 145-150. 2007-10-27T17:05:39-00:00 145 150 relativity http://www.citeulike.org/user/norris/article/1829644 <i>Acta Mechanica, Vol. 161, No. 1. (6 March 2003), pp. 103-125.</i><br /><br />Summary. Remarkable hidden interrelations can be shown to exist between some fundamental principles of continuum mechanics if a four-dimensional formalism is used, e.g., if time is placed on the same footing as space. To exhibit these properties, the special theory of relativity supplies the proper framework. The fully relativistic energy-momentum tensor and the associated Euler-Lagrange equations are formulated for an elastic solid and for a perfect fluid as a limiting case. Approximate relativistic balance and conservation laws are then derived by expanding the exact relativistic relations in series of powers of the ratio of the velocity of motion to the velocity of light. Several orders of approximation are examined in detail, employing both the Eulerian and the Lagrangian description. This permits to gain new insight into the interrelated structure of the basic laws of continuum mechanics, such as the balance (or conservation) of mass, energy, physical (linear) momentum and material (linear) momentum. As a by-product, a hierarchy of approximate theories of continua is established whose velocity of motion is comparable to the velocity of light. On the four-dimensional formalism in continuum mechanics R Kienzler G Herrmann doi:10.1007/s00707-002-0984-z Acta Mechanica, Vol. 161, No. 1. (6 March 2003), pp. 103-125. 2007-10-27T17:00:35-00:00 2003 Acta Mechanica 161 1 103 125 relativity