Difference between revisions of "Rotation indicatrix"
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''rotation diagram'' | ''rotation diagram'' | ||
| − | One of the twelve [[Darboux surfaces|Darboux surfaces]] associated with the [[Infinitesimal deformation|infinitesimal deformation]] of a surface. It is the set of points in space described by a position vector | + | One of the twelve [[Darboux surfaces|Darboux surfaces]] associated with the [[Infinitesimal deformation|infinitesimal deformation]] of a surface. It is the set of points in space described by a position vector $ \mathbf y $ |
| + | which are parallel to the rotation vector (instantaneous angular velocity) defined by the equation $ d \mathbf z = [ \mathbf y d \mathbf x ] $, | ||
| + | where $ \mathbf z $ | ||
| + | is the velocity vector of the infinitesimal deformation of the surface described by the position vector $ \mathbf x $. | ||
| + | The displacement indicatrix (displacement diagram) is defined in a similar manner by the displacement vector $ \mathbf s = \mathbf z - [ \mathbf y \mathbf x ] $. | ||
====References==== | ====References==== | ||
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> N.V. Efimov, "Qualitative questions of the theory of deformations of surfaces" ''Uspekhi Mat. Nauk'' , '''3''' : 2 (1948) pp. 47–158 (In Russian)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> S.E. Cohn-Vossen, "Some problems of differential geometry in the large" , Moscow (1959) (In Russian)</TD></TR></table> | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> N.V. Efimov, "Qualitative questions of the theory of deformations of surfaces" ''Uspekhi Mat. Nauk'' , '''3''' : 2 (1948) pp. 47–158 (In Russian)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> S.E. Cohn-Vossen, "Some problems of differential geometry in the large" , Moscow (1959) (In Russian)</TD></TR></table> | ||
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====Comments==== | ====Comments==== | ||
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====References==== | ====References==== | ||
<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> G. Darboux, "Leçons sur la théorie générale des surfaces et ses applications géométriques du calcul infinitésimal" , '''1–4''' , Chelsea, reprint (1972)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> M. Spivak, "A comprehensive introduction to differential geometry" , '''1979''' , Publish or Perish pp. 1–5</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top"> N.V. Efimov, "Qualitative problems of the theory of deformation of surfaces" , Amer. Math. Soc. (1951) (Translated from Russian)</TD></TR></table> | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> G. Darboux, "Leçons sur la théorie générale des surfaces et ses applications géométriques du calcul infinitésimal" , '''1–4''' , Chelsea, reprint (1972)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> M. Spivak, "A comprehensive introduction to differential geometry" , '''1979''' , Publish or Perish pp. 1–5</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top"> N.V. Efimov, "Qualitative problems of the theory of deformation of surfaces" , Amer. Math. Soc. (1951) (Translated from Russian)</TD></TR></table> | ||
Revision as of 08:12, 6 June 2020
rotation diagram
One of the twelve Darboux surfaces associated with the infinitesimal deformation of a surface. It is the set of points in space described by a position vector $ \mathbf y $ which are parallel to the rotation vector (instantaneous angular velocity) defined by the equation $ d \mathbf z = [ \mathbf y d \mathbf x ] $, where $ \mathbf z $ is the velocity vector of the infinitesimal deformation of the surface described by the position vector $ \mathbf x $. The displacement indicatrix (displacement diagram) is defined in a similar manner by the displacement vector $ \mathbf s = \mathbf z - [ \mathbf y \mathbf x ] $.
References
| [1] | N.V. Efimov, "Qualitative questions of the theory of deformations of surfaces" Uspekhi Mat. Nauk , 3 : 2 (1948) pp. 47–158 (In Russian) |
| [2] | S.E. Cohn-Vossen, "Some problems of differential geometry in the large" , Moscow (1959) (In Russian) |
Comments
References
| [a1] | G. Darboux, "Leçons sur la théorie générale des surfaces et ses applications géométriques du calcul infinitésimal" , 1–4 , Chelsea, reprint (1972) |
| [a2] | M. Spivak, "A comprehensive introduction to differential geometry" , 1979 , Publish or Perish pp. 1–5 |
| [a3] | N.V. Efimov, "Qualitative problems of the theory of deformation of surfaces" , Amer. Math. Soc. (1951) (Translated from Russian) |
How to Cite This Entry:
Rotation indicatrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Rotation_indicatrix&oldid=15111
Rotation indicatrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Rotation_indicatrix&oldid=15111
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article