The moving power of Mathematical invention is not reasoning but Imagination!!! https://twitter.com/JamesClerkMax11/status/921759795345891328/photo/1pic.twitter.com/Czf46FFMXT pic.twitter.com/iuxSwUZKZ7
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The moving power of Mathematical invention is not reasoning but Imagination!!! https://twitter.com/JamesClerkMax11/status/921759795345891328/photo/1pic.twitter.com/Czf46FFMXT pic.twitter.com/iuxSwUZKZ7
Parabola is described by quadratic function and chain curve by hyperbolic (transcendental) function.
Junguis has considered chain with friction... Galelio had considered frictionless chain(Parabolic) for the ease of mathematical modelling ...
No, both solutions consider the chain to be perfectly flexible (which is what you meant by "frictionless"). The parabolic solution assumes equal weight force per unit of horizontal distance, whereas the catenary solution assumes equal weight force per unit length.
Supporting details on Alysoid (catenary)... http://mathworld.wolfram.com/Catenary.html
in fairness to Galileo, calculus wasn't even invented in his time.. let alone the calculus of variations
cosinus hyperbolique !
But when we throw a Stone.. is it a Parabola?
Mathematically yes, but in practice - on earth - no (mainly because of air resistance). For small throws on a big planet a parabola is a good-enough estimation.
Hyperbolic cosine :D
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