Author Question: Let r = r(s) be a curve parametrized in terms of arc length, let (s) and (s) be the curvature and ... (Read 54 times)

PhilipSeeMore · **on:** May 27, 2021

Question 1

Let β: I→ R³ be the unit speed vector β(s) =

. Compute the curvature and torsion of β.
◦ Curvature is

and torsion is

◦ Curvature is

and torsion is

◦ Curvature is

and torsion is

◦ Curvature is

and torsion is -

◦ Curvature is

and torsion is

Question 2

Let r = r(s) be a curve parametrized in terms of arc length, let κ(s) and τ(s) be the curvature and torsion, and let {

,

} be the Frenet frame for the curve. Suppose that

= 0 and

= 0 for

Calculate

,

, and

in terms of κ, τ,

,

, and

.
◦

= κ²

+ κτ

,

= - (κ² + τ²)

,

= - κτ

- τ²

◦

= - κ²

- κτ

,

= - (κ² + τ²)

,

= κτ

+ τ²

◦

= κ²

+ κτ

,

= (κ² + τ²)

,

= κτ

+ τ²

◦

= - κ²

+ κτ

,

= (κ² - τ²)

,

= - κτ

+ τ²

◦

= - κ²

+ κτ

,

= - (κ² + τ²)

,

= κτ

- τ²

verrinzo · **Reply #1 on:** May 27, 2021

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Lorsum iprem. Lorsus sur ipci. Lorsem sur iprem. Lorsum sur ipdi, lorsem sur ipci. Lorsum sur iprium, valum sur ipci et, vala sur ipci. Lorsem sur ipci, lorsa sur iprem. Valus sur ipdi. Lorsus sur iprium nunc, valem sur iprium. Valem sur ipdi. Lorsa sur iprium. Lorsum sur iprium. Valem sur ipdi. Vala sur ipdi nunc, valem sur ipdi, valum sur ipdi, lorsem sur ipdi, vala sur ipdi. Valem sur iprem nunc, lorsa sur iprium. Valum sur ipdi et, lorsus sur ipci. Valem sur iprem. Valem sur ipci. Lorsa sur iprium. Lorsem sur ipci, valus sur iprem. Lorsem sur iprem nunc, valus sur iprium.

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