On Janmann-Zaremba time derivative

Adam Piskorek. "On Janmann-Zaremba time derivative." Mathematica Applicanda 24.38 (1995): null. <http://eudml.org/doc/292976>.

@article{AdamPiskorek1995,
abstract = {This is an extended discussion of the introduction and role played by the so-called co-rotational derivative (also called the Jaumann derivative in Germany and, rightfully, the Zaremba derivative in Poland) and other "objective'' time derivatives of geometrical objects as they appear in continuum physics. This is achieved in a somewhat abstract formalism starting with clearly defined "spatial" and "material" notions, the differentiable-manifold definition of deformation tensors, and the notions of parallel transport and Lie derivative. The notion of "objectivity'' (as common in continuum mechanics since the pioneering work of W. Noll) and Piola transformations follow next. The paper ends with a reminder on local balance equations and objective constitutive equations such as those of the time-rate type. It seems that the author does not know the famous book of J. E. Marsden and T. J. R. Hughes [Mathematical foundations of elasticity, corrected reprint of the 1983 original, Dover, New York, 1994; MR1262126], where most of the given material can be found.},
author = {Adam Piskorek},
journal = {Mathematica Applicanda},
keywords = {Constitutive equations; Applications to physics},
language = {eng},
number = {38},
pages = {null},
title = {On Janmann-Zaremba time derivative},
url = {http://eudml.org/doc/292976},
volume = {24},
year = {1995},
}

TY - JOUR
AU - Adam Piskorek
TI - On Janmann-Zaremba time derivative
JO - Mathematica Applicanda
PY - 1995
VL - 24
IS - 38
SP - null
AB - This is an extended discussion of the introduction and role played by the so-called co-rotational derivative (also called the Jaumann derivative in Germany and, rightfully, the Zaremba derivative in Poland) and other "objective'' time derivatives of geometrical objects as they appear in continuum physics. This is achieved in a somewhat abstract formalism starting with clearly defined "spatial" and "material" notions, the differentiable-manifold definition of deformation tensors, and the notions of parallel transport and Lie derivative. The notion of "objectivity'' (as common in continuum mechanics since the pioneering work of W. Noll) and Piola transformations follow next. The paper ends with a reminder on local balance equations and objective constitutive equations such as those of the time-rate type. It seems that the author does not know the famous book of J. E. Marsden and T. J. R. Hughes [Mathematical foundations of elasticity, corrected reprint of the 1983 original, Dover, New York, 1994; MR1262126], where most of the given material can be found.
LA - eng
KW - Constitutive equations; Applications to physics
UR - http://eudml.org/doc/292976
ER -