Catenary problem:
I am going to animate a variable (chain) catenary, where a tugboat drag a floating rigid object.

My problem is how to make the catenary line attached in both ends, to the ridgid object and to the moving tugboat (sailing away from the rigid object and the boat roll and pitch on the waves). The catenary line will stretch and change shape following the tugboat motions.

I am thinking about using constraints, but what type constraint will work in this case? And how to do this? I need some instructions.
The chain can then probably use the (variable) catenary line as path for the PathDeform modifier - or what do you think?

Any thoughts and suggestions are very welcome, thanks!

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how about a line with about 6 vertices. use soft selection and set it so that the vertex at the stationary side is white. linked Xform the white vertex to the stationary dummy, apply spline select and another linked Xform for the red vertex and attach it to the animated dummy

Max 2.5 through 2014, win7 64bit.
GIGABYTE GV-N580UD-3GI GeForce GTX 580 3072MB
Intel Core i7-3930K 3.2GHz
4Gx8 CORSAIR CML16GX3M4A1600C9

try changing the soft select value and/or the number of vertices and also witch vertices you attach to the dummy. i only used this technique to simulate stretching of wires. it may not work for you specific case. you may also consider adding some constrains for the weight off the chain

Max 2.5 through 2014, win7 64bit.
GIGABYTE GV-N580UD-3GI GeForce GTX 580 3072MB
Intel Core i7-3930K 3.2GHz
4Gx8 CORSAIR CML16GX3M4A1600C9