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Equations for the Brachistochrone

Brachistochrone Part IV
Deposit # 60

Bernoulli first stated this problem in 1696.
The following are notes prepared for the undergraduate Analysis class MATH 466, Advanced Calculus II, at California State University, Los Angeles.  The intent was to give the students a taste of the uses of some of the Analysis they had learned.  The National Curve Bank - A MATH Archive thanks Dr. Michael Hoffman for making the Euler-Lagrange approach to the brachistochrone available to others.   []

The Brachistochrone Problem
Suppose  A  and  B  are two points,  A  lower than  B.  Find the shape of the wire joining them such that a frictionless bead sliding from  A  to  B  does so in minimum time.

Hoffman Page 1

Hoffman Part 2

Hoffman Part 3

Hoffman Part 5

Hoffman Part 6

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Brachistochrone Part II

Brachistochrone Part III