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jweiss55
07-14-2005, 08:10 AM
In solid mechanics, a homogeneous deformation / transformation /
deformation map is one where the components of the deformation gradient
tensor do not have any dependence on the spatial coordinates. A more
intuitive definition is that a homogeneous deformation maps straight
lines into straight lines. This admits homogeneous shear, stretching,
compression, rotation, translation, etc.

A rigid deformation / transformation / deformation map is one that obeys
the above definition but also can be decomposed into a proper orthogonal
rotation and a translation (again, both constant in space).

Any decent textbook on continuum mechanics will confirm these definitions.

The whole idea of a "matrix", whether 4x4 or 3x3 + a 3x1 translation, is
simply a computational tool.

Jeff

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Jeffrey A. Weiss, Ph.D.
Department of Bioengineering, University of Utah
jeff.weiss@utah.edu http://hodad.bioen.utah.edu/~weiss/mrl