Hello!

Can somebody tell me what curve is this:

(a t; b sin t; c cos t), t e R

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- May 12th 2012, 12:08 PMmboricgsWhat curve is this?
Hello!

Can somebody tell me what curve is this:

(a t; b sin t; c cos t), t e R - May 12th 2012, 01:42 PMSorobanRe: What curve is this?
Hello, mboricgs!

Quote:

Can somebody tell me what curve is this:

. . $\displaystyle (a t,\; b\sin t,\; c\cos t),\; t \in R$

It is an ellipsoidal helix centered on the x-axis.

- May 27th 2012, 06:51 AMmboricgsRe: What curve is this?
what is equation of this curve without t?

- May 27th 2012, 06:56 AMProve ItRe: What curve is this?
$\displaystyle \displaystyle \begin{align*} x &= a\,t \\ \\ y &= b\sin{t} \\ \frac{y}{b} &= \sin{t} \\ \frac{y^2}{b^2} &= \sin^2{t} \\ \\ z &= c\cos{t} \\ \frac{z}{c} &= \cos{t} \\ \frac{z^2}{c^2} &= \cos^2{t} \\ \\ \frac{y^2}{b^2} + \frac{z^2}{c^2} &= \sin^2{t} + \cos^2{t} \\ \frac{y^2}{b^2} + \frac{z^2}{c^2} &= 1 \end{align*}$

So that means you have ellipses on the $\displaystyle \displaystyle \begin{align*} y-z \end{align*}$ plane, and as you change $\displaystyle \displaystyle \begin{align*} t \end{align*}$, the x values increase, which means it wraps around the $\displaystyle \displaystyle \begin{align*} x \end{align*}$ axis, creating an elliptical helix. - May 27th 2012, 07:00 AMmboricgsRe: What curve is this?
Thank you. What about flexion and torsion? Are they constant?

- May 27th 2012, 07:14 AMmboricgsRe: What curve is this?
- May 28th 2012, 07:26 AMmboricgsRe: What curve is this?
Can someone tell me hot to do that in wolframalpha?