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Orthogonal Trajectory

An orthogonal trajectory of a family of plane curves is a curve that intersects every member of the family at a right angle. If the family has a differential equation

y^'=F(x,y),

then its orthogonal trajectories satisfy y^'=-1/F(x,y) wherever F is finite and nonzero. Equivalently, if the given family consists of level curves u(x,y)=c, its orthogonal trajectories follow the gradient field del u.

See also

Gradient, Level Curve, Right Angle

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References

Boyce, W. E. and DiPrima, R. C. Elementary Differential Equations and Boundary Value Problems, 9th ed. Hoboken, NJ: Wiley, 2009.

Cite this as:

Weisstein, Eric W. "Orthogonal Trajectory." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/OrthogonalTrajectory.html

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