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Catenary curve in instrument backs
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sdantonio
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Joined: 09 Apr 2007
Posts: 35
Location: Bellingham, Massachusetts, USA

PostPosted: Tue Apr 10, 2007 11:16 am    Post subject: Reply with quote

JWH wrote:
"The name catenary curve describes a family of curves based on the cosh function, not just a single curve. It has also been described as the curve formed by allowing a chain to hang freely. "

Contrary to what you've written, a catenary curve is not a family of curves but is a single curve only varied by scale with coordinants that don't change in relationship to themselves. The formula stays the same whether I 'pull your chain' or someone else does, rendering it slack or taut.



A set of curves whose equations are of the same form but which have different values assigned to one or more parameters in the equations. Families of curves arise, for example, in the solutions to differential equations with a free parameter (Harris and Stocker 1998, p. 649). http://mathworld.wolfram.com/FamilyofCurves.html

In the catenary isn’t “a” one such free variable?

x(t) = t

y= cosh (t/a)
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