For a plane curve, the tangential angle 
is defined by
 |
(1)
|
where 
is the arc length and 
is the radius of curvature.
The tangential angle is therefore given by
 |
(2)
|
where 
is the curvature. For a plane curve 
, the tangential angle 
can also be defined by
![(r^'(t))/(|r^'(t)|)=[cos[phi(t)]; sin[phi(t)]].](https://speed.lescigales.org/xypor/index.php?q=aHR0cHM6Ly9tYXRod29ybGQud29sZnJhbS5jb20vaW1hZ2VzL2VxdWF0aW9ucy9UYW5nZW50aWFsQW5nbGUvTnVtYmVyZWRFcXVhdGlvbjMuc3Zn) |
(3)
|
Gray (1997) calls 
the turning angle instead of the tangential angle.
See also
Arc Length,
Curvature,
Plane Curve,
Radius
of Curvature,
Torsion
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References
Gray, A. "The Turning Angle." §1.7 in Modern
Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca
Raton, FL: CRC Press, pp. 19-20, 1997.Lawrence, J. D. A
Catalog of Special Plane Curves. New York: Dover, pp. 4 and 22, 1972.Yates,
R. C. A
Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards,
p. 124, 1952.Referenced on Wolfram|Alpha
Tangential Angle
Cite this as:
Weisstein, Eric W. "Tangential Angle."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TangentialAngle.html
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