Catenary = Physic + Math + IT

[ValeryOchkov]

It is the site of the article "Catenary = Physic + Math + IT" (color picture + Mathcad sheet)

Two students - Three smilesReal catenaryTwo vectorsParabola and 3 pointsParabola thru 3 pointsParabola near 10 pointsCatenary and 10 points

Physical Mathematics

[ValeryOchkov]

We can have thru 5 points a hyperbola (D<0), an ellipse (D>0) or (good chance D=0) a parabola:

[ValeryOchkov]

The solution with the Find Function: the partial vectorization!

And second - we can add more points, change the Find function to MinErr function and get not the interpolation but approximation!

[ValeryOchkov]

With lsolve function! We do not need guess values! But how can we add more points (6, 7, 9 etc) without change the Matrix M and the vector v?

 

[ValeryOchkov]

[ValeryOchkov]

One more experiment (see please the attached Mathcad 15 file)

[ValeryOchkov]