[rotation] nomenclature

Alain Cochard alain at geophysik.uni-muenchen.de
Tue Jan 29 15:20:02 CET 2008


Alberto Castellani writes:

 > The picture enclosed in the document of Evans seems to establish
 > that 6 independent degrees of freedom are assigned to each
 > point. In continuum mechanics, any nodal point has three degrees of
 > freedom, in the following the translations along x, y, and z
 > axes. Rotations are derivative with respect to translations.

Maybe here too, it is a matter of terminology, but it seems to me that
as soon as you talk about derivatives, you implicitly consider some
neighborhood, even if infinitely small, *around* a point, and no
longer the point itself per se.  

So I'd say that if one restricts oneself to a punctual point (if I may
say), then it's perfectly appropriate to speak about 6 degrees of
freedom (whether or not it was John's intention; John, I hope you will
comment on that).

I would add that this is true only for a rigid body.  For a deformable
body there are 6 additional strain quantities (that may of course also
be determined by measurements in some neighborhood -- array
measurements).

Regards,
Alain



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