Vector Calculus : Vector Valued Functions, Arc Length and Curvature

Related BrainMass Solutions

• 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.

• 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

• Vectors and Curvature

  The curvature is defined as: Where is the tangential angle and is the arc length: Then, for parametric relations: We get: Now, by definition: Therefore: But: Thus: Combining the results

• Vector Cross Product and Arc length

  Vector Cross Product and Arc length are investigated.

• Multiple Integrals and vector calculus

  238942 Multiple Integrals and vector calculus Multiple Integrals and vector calculus. 1.

• Solutions to Various Problems in Vector Calculus

  We solve various problems in vector calculus.

• Vector calculus/ the geometry of real-valued functions

  63800 Vector Calculus: The Geometry of Real-Valued Functions Describe the surfaces in R3 of the equation: y^2 = x^2 + z^2.

• Arc Length of a Parametric Curve

  The length of the curve on the interval is, Then the arc length is The arc length of a parametric curve is found. The solution is detailed and well presented.

• Finding Curvature at a Point

  So in your case, have the vector: vector r(t) = t i + 1/2 t^2 j + 1/3 t^3 k What is the curvature at t = 1 and how do I calculate this? Find r'(t) and r''(t), first and second derivative of the r(t) wrt t.