Envelope Theorem in Generalized Calculus
In the calculus of variations, the envelope theorem relates evolutes to single paths. This was first proved by Jean Gaston Darboux and Ernst Zermelo (1894) and Adolf Kneser (1898). The theorem can be stated as follows:
"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, JOA = JOB + JBA."
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