Mechanical Engineering: Ch 10: Forces on Cables (16 of 33) Catenary - Inverse Hyperbolic Sine

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In this video I will derive y=sinh-1(y) and therefore x=sinh(y) where y=vertical sag of a catenary cable.

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Комментарии
Автор

This seems to indicate that if you know X, then you can calculate Y. But Y would depend on the tension in the cable. Y could be small or large. You need the parameter for T or for the angle at the end.

lesross
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I don’t like how you introduced the hyperbolic functions. You should’ve started off introducing hyperbolic cosine, because the shape of a catenary follows y = a*cosh(x/a), then you should’ve introduced how hyperbolic sin gives the arc length of the catenary.

I don’t think that y = sinh^-1(x) is the equation of the catenary. that doesn’t make sense.

JGambrosia
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Why y = sinh if in your next videos y = cosh?

АК-ОлексійКозакевич
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it's difficult to understand when you're blocking your equation while explaining where, why and how.

igleedejarme
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Shouldn't it be y = cosh(x)? I plotted sinh(y) = x on wolfram and it gave some weird curve.

ottomota
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That integral is equal to hyperbolic sin inverse of (x/a) 😒

anishsharma