A brachistochrone is characterized by F_n = mv²/R, and for central forces the wire can be replaced by a designed magnetic field, reducing the problem to direct integration.
Dynamics of a Particle
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Facets of Brachistochronic Trajectories
A brachistochrone is characterized by F_n = mv²/R, and for central forces the wire can be replaced by a designed magnetic field, reducing the problem to direct integration.