Quote:
Originally Posted by Richard
The cycloid curve solves the classic (~300 year old) brachistochrone problem. The important feature of a such a "curve of fastest descent" it that it converts all of the falling particle's energy from vertical to horizontal motion in the least time. Applying the same criterion in reverse, to convert a minibot's energy from horizontal to (upward) vertical motion, will yeild the same curve.
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The cycloid is optimal for an unpowered e.g. object, such as a rolling ball. Is it still optimal when the object is powered?