Equations for double helix in parametric form

skr3178

New member
Joined
Dec 28, 2020
Messages
2
Hi,
I am working on a double helix problem for which I would like determine the equation.
I have been able to find a few hints on other forums (Double helix)but they aren't in parametric form. In am specifically looking to determine the equation similar to picture as shown on the right of the precatenanes image.

I would appreciate any help on this.
Thanks so much
 

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Cubist

Full Member
Joined
Oct 29, 2019
Messages
796
I have a recommendation, detailed below, but it's probably biassed because I'm a programmer !

Despite this problem having a very strong mathematical element, it's much easier to tackle it using a computer programming language. I used Octave (a Matlab-like program) to generate the image below. This is a good approach because you can:-
- create a "black box" of re-usable functionality (to generate a spiral around a path)
- define intermediate/ temporary variables within functions to make subsequent expressions easier to read
- immediately plot your results to see if you're on the right track

20200221_spring.png

Your problem breaks nicely down into blocks of functionality. One important function to write is:- given a point on a path (and that point's direction/velocity vector) then return a new point that is on a spiral that "orbits" in a helix around the input path (for different "t" amounts). This function could also return a velocity vector for the new point. When this is done you could call this function a second time to create a spiral around a spiral around a path.

If you really have to, after writing a successful computer program to do this - then you could then use a CAS to back-substitute all intermediate variables so that you end up with a (truly horrendous) set of 3 expressions (x,y,and z) that are purely in terms of t.

Since this is a help-site I won't just hand out my code. But I'll give you a hint, first of all write some code that produces the first helix and plots it using "scatter3()".
 
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