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Tangential Angle

For a plane curve, the tangential angle phi is defined by

rhodphi=ds,

(1)

where s is the arc length and rho is the radius of curvature. The tangential angle is therefore given by

phi=int_0^ts^'(t)kappa(t)dt,

(2)

where kappa(t) is the curvature. For a plane curve r(t), the tangential angle phi(t) can also be defined by

(r^'(t))/(|r^'(t)|)=[cos[phi(t)]; sin[phi(t)]].

(3)

Gray (1997) calls phi 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." ยง1.7 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.

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Tangential Angle

Cite this as:

Weisstein, Eric W. "Tangential Angle." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TangentialAngle.html

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