View source for Swerve of a curve

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''self-rotation of a curve''

The part of the variation of the rotation of a curve on an irregular surface not caused by the concentration of the integral curvature of the surface on the set of points of the curve. For a simple arc  $  L $, 
the swerve is equal to  $  ( \sigma _ {r} + \sigma _ {l} - \Omega )/2 $, 
where  $  \sigma _ {r} , \sigma _ {l} $
are the variations under right and left traversal of  $  L $, 
while  $  \Omega $
is the variation of the curvature of  $  L $
as a set. Curves with swerve zero are called quasi-geodesic curves (cf. [[Quasi-geodesic line]]).

====References====
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<TR><TD valign="top">[1]</TD> <TD valign="top">  A.D. Aleksandrov,   V.V. Strel'tsov,   "Isoperimetric problems and estimates of the length of a curve on a surface"  ''Proc. Steklov Inst. Math.'' , '''76'''  (1965)  pp. 81–99  ''Trudy Mat. Inst. Steklov.'' , '''76'''  (1965)  pp. 67–80</TD></TR>
<TR><TD valign="top">[a1]</TD> <TD valign="top">  H. Busemann,   "Convex surfaces" , Interscience  (1958)  pp. Chapt. III, Sect. 15</TD></TR>
</table>