Quote:
Originally Posted by EricVanWyk
The cycloid is optimal for an unpowered e.g. object, such as a rolling ball. Is it still optimal when the object is powered?
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To answer this one, begin by writing an equation for the minibot's speed as a function of its height. How does the power contributed by the minibot motor(s) influence this speed function? Does the minibot's initial speed at the moment it crosses the deployment cylinder (tower base) matter? If the speed function has the same form as that of the unpowered object, namely the inverse square root of the object's gravitational potential, then the curve of quickest ascent will be a cycloid. See
this reference for Bernoulli's reasoning, based on conservation of energy.
If you like this kind of problem, try your university's course in Calculus of Variations -- generally a graduate-school topic for engineers, or an advanced class for students of applied math.
__________________
Richard Wallace
Mentor since 2011 for FRC 3620 Average Joes (St. Joseph, Michigan)
Mentor 2002-10 for FRC 931 Perpetual Chaos (St. Louis, Missouri)
since 2003
I believe in intuition and inspiration. Imagination is more important than knowledge. For knowledge is limited, whereas imagination embraces the entire world, stimulating progress, giving birth to evolution. It is, strictly speaking, a real factor in scientific research.
(Cosmic Religion : With Other Opinions and Aphorisms (1931) by Albert Einstein, p. 97)