Bernoulli's lightray solution for the brachistochrone problem from ...
Bernoulli's lightray solution for the brachistochrone problem from ...
Bernoulli's lightray solution for the brachistochrone problem from ...
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Gravitational refraction indexBack to <strong>brachistochrone</strong> <strong>problem</strong>Gravitational energy 1 2 (v(y))2 +gy = 0 (n(y)) 2 = 1−2gy , <strong>for</strong>y < 0 reduced canonical equationsẏ = −2gyp yṗ y = g(p 2 y +I 2 )Level curve H I (y,p y ) = E has <strong>for</strong>my = − 1 ( ) Eg p 2 y +I 2(4)
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