/sci/ - Science & Math

[Anonymous No.6084172]

Let's say you want to find the curvature of a vector valued function, as a function of time.

But let's also say that your position function is messy. The derivatives chain out, and the magnitudes don't simplify.

How should you approach these kinds of problems, especially if the commonly used v cross a formula gets particularly messy?

[Anonymous No.6084175]

Do you even know the definition of curvature?

[Anonymous No.6084185]

> curvature of a vector valued function
que?
> How should you approach these kinds of problems, especially if the commonly used v cross a formula gets particularly messy?
Use many reference frames. store rotation matrices for later.

[Anonymous No.6084229]

>>6084175
Sure, but if your position vector is messy, getting something in terms of arc length will be even worse.

>>6084185
As in, r(t) = <f(t), g(t), h(t)>?
Anyway, I don't have much linear algebra to work with.

[Anonymous No.6084234]

>>6084175
>>6084185
>>6084229

curvature is le second derivative.

I am guessing you are looking at a polynomial function (which can usually be expressed as a single term & even if you aren't, you can estimate it using summed sines with phase shifts), but if you aren't then you are probably looking for curvature of something defined piecewise

[Anonymous No.6084264]

>>6084234
Wait, really? Let's say you're solving simply in terms of t - wouldn't you have to scale the tangent and normal vectors down to unit vectors to get the right values?

This has been my biggest issue - dividing out the magnitude of the first derivative made the second derivative a huge pain. So is it correct to say that k(t) = r''(t) / |r''(t)|