Given-the-space-curve-r-r-t-show-that-its-torsion-is-given-by-r-r-r-r-r-2-It-may-help-to-know-that-its-curvature-is-numerically-given-by-r-r-

Question Number 5115 by Yozzii last updated on 14/Apr/16

G i v e n t h e s p a c e c u r v e r = r (t), s h o w

t h a t i t s t o r s i o n τ i s g i v e n b y

τ = \frac{\dot{r} ∙ \overset{. .}{r} \times \overset{\dots}{r}}{∣ \dot{r} \times \overset{. .}{r} ∣^{2}} . I t m a y h e l p t o k n o w t h a t i t s

c u r v a t u r e i s n u m e r i c a l l y g i v e n b y κ = \frac{∣ \dot{r} \times \overset{. .}{r} ∣}{∣ \dot{r} ∣^{3}} .

\dot{r} i s d i f f e r e n t i a t i o n o f r o n c e w i t h

r e s p e c t t o t .