Abstract
The time required for a particle to slide frictionlessly down a set of ramps connected end to end can be minimized numerically as a function of the coordinates of the connection points between ramps and compared to the exact cycloidal solution of the brachistochrone problem. It is found that a set of just three joined ramps over a large range of geometrical aspect ratios has a descent time within 5% of the optimal cycloid. The special case where the particle starts and ends at the same height has sufficient symmetry that it can be analyzed analytically using algebra alone. The level of analysis is appropriate to an undergraduate classical mechanics course.
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