Curvature of the curve and torsion of the curve

Related BrainMass Solutions

• Curvature and torsion of a curve

  12297 Curvature and torsion of a curve For the curve: r = ( 2abt, a^2 log t, b^2t^2 ), show that: κ = - τ = 2abt/(a^2 + 2b^2t^2)^2 where κ = curvature of the curve τ = torsion of the curve.

• binormal

  380576 Binormal Twisted Curve Suppose a twisted curve is defined in terms of the arclength s by r(s)=sech(?)cos(s)i+sech(?)sin(s)j+tanh(?)k, where ? is a constant parameter.

• Elliptic Curves

  Show that the greatest common divisor of (psi_3)(x) and "x^5 -x" is "x(x-1)." 3. Use part (2) to show that the 3-torsion points in E(F5) are {Origin,(0,1),(0,-1)}."

• Curvature of a curve in space

  50086 Curvature of a Curve in Space The curvature of a curve in space r(t) is given by k(t) = | r'(t) à? r''(t) | / | r'(t) |^3 . Consider now the curve r(u) = r(sigma(u)), given by the reparametrization t = sigma(u) of the initial curve.

• Vector Analysis : Construction of a Plane Curve

  We would like to construct a plane curve B(s) with curvature K(s)..... HINT: Use the Fundamental Theorem of Calculus to show B has unit speed and then compute dT/ds. Problem: I.

• Radius of Curvature

  409880 Radius of Curvature (a) Find the point of intersection of the line containing the points (3; 2; 1) and (4; 3; 3), and the plane containing the points (5; 4; 2), (3; 1; 6) and (6; 5; 3).

• Charecteristics of a curve

  Let g(t) = (a cos (wt) , a sin(wt) , bt) t>0 Find explicitly the arc length parametrization h(s) of the curve Find the unit tangent and principle normal vectors at an arbitrary point h(s) Find the curvature k(s) Please see the attached file for

• Curvature

  70359 Curvature I am asked to find the curvature at the point where t=1 of the curve given by: vector r(t) = t i + 1/2 t^2 j + 1/3t^3 k How do I do this problem and what is the final answer?

• Finding Curvature

  For the less general case of a plane curve given explicitly as: y = f(x) the curvature is Find the curvature 1. y =x^3 So the curvature is 2. y =cosx The curvature is The expert finds the curvature of a function.