TOPICS
Search

Envelope Theorem


Relates evolutes to single paths in the calculus of variations. Proved in the general case by Darboux and Zermelo in 1894 and Kneser in 1898. It states: "When a single parameter family of external paths from a fixed point O has an envelope, the integral from the fixed point to any point A on the envelope equals the integral from the fixed point to any second point B on the envelope plus the integral along the envelope to the first point on the envelope, J_(OA)=J_(OB)+J_(BA)."


Explore with Wolfram|Alpha

References

Kimball, W. S. Calculus of Variations by Parallel Displacement. London: Butterworth, p. 292, 1952.

Referenced on Wolfram|Alpha

Envelope Theorem

Cite this as:

Weisstein, Eric W. "Envelope Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EnvelopeTheorem.html

Subject classifications