The Brachistochrone Problem: Show that if the particle is projected with an initial kinetic energy 1/2 m v02 that the brachistochrone is still a cycloid passing through the two points with a cusp at a height z above the initial point given by v02 = 2gz.

The Brachistochrone Problem: Show that if the particle is projected with an initial kinetic energy 1/2 m v02 that the brachistochrone is still a cycloid passing through the two points with a cusp at a height z above the initial point given by v02 = 2gz.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter6: Some Methods In The Calculus Of Variations

Section: Chapter Questions

Problem 6.15P

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Question

The Brachistochrone Problem: Show that if the particle is projected with
an initial kinetic energy 1/2 m v₀²that the brachistochrone is still a cycloid
passing through the two points with a cusp at a height z above the initial
point given by v₀² = 2gz.

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