Thanks, but I want this chain keep the same length always (for example: length=5) and when A' and B' are 5 grids away from each other, the chain should look like a segment.
Could you please re-issue the sheet without animation, but showing the point to move manually (via mouse)? I've faced the drawback shown below. Thank you
The same question 
The catenary function should be manipulated through a slider (t) and any desired parameter, here a=10t/cosh(4), as per attachements.
Be aware! The horizontal position of the chain can"t be reached, due to function degeneration into the line y=1.
Cheers
Thanks, but I want this chain keep the same length always (for example: length=5) and when A' and B' are 5 grids away from each other, the chain should look like a segment.
this is very difficult but I will try
meantime I did an approx work
the lenght is near 4
it is undefined when C is (0,0) but this can be solved with if[] comand and segment
I think the original is approx also
Thank you very very much mathmagic!!! You are great!!!
Please let me know if you made it perfect (exactly 4).
have you enough with this trick?
four new objects seem to solve the problem
I dilated the objects of previous work for length=4
I did not get solution with integral equations
Could you please re-issue the sheet without animation, but showing the point to move manually (via mouse)? I've faced the drawback shown below. Thank you
the animated point is C . C is hidden. download the worksheet and "desanimate" C
show C and hide C'_1. both are near
new worksheet using the general catenaria f(x)= 1/a cosh(a x) because the lenght is calculated =1/a sinh(a x)
the only approx calculus is for solving equations
https://www.geogebra.org/m/UYxnWced
Awesome!!!
...the general catenaria f(x)= 1/a cosh(a x) because the lenght is calculated =1/a sinh(a x) ...
Sure! This is a valid property of catenary. Further comments below
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