Purchase Solution

Curvature and torsion of a curve

Not what you're looking for?

Ask Custom Question

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.

Purchase this Solution
Solution Summary

This solution is comprised of a detailed explanation for finding the curvature of the curve and torsion of the curve.
It contains step-by-step explanations to find the curvature and torsion of the curve, r = ( 2abt, a^2 log t, b^2t^2 ).

Solution provided by:
Thokchom Sarojkumar Sinha, MSc
Education
  • BSc, Manipur University
  • MSc, Kanpur University
Recent Feedback
  • "Thanks this really helped."
  • "Sorry for the delay, I was unable to be online during the holiday. The post is very helpful."
  • "Very nice thank you"
  • "Thank you a million!!! Would happen to understand any of the other tensor problems i have posted???"
  • "You are awesome. Thank you"
Purchase this Solution
Free BrainMass Quizzes
Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Probability Quiz

Some questions on probability

View More Free Quizzes
Related BrainMass Solutions

  • Curvature of the curve and torsion of the curve

    This solution is comprised of a detailed explanation for finding the curvature of the curve and 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.

  • 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.

  • Vector Analysis : Construction of a Plane Curve

    We would like to construct a plane curve (s) with curvature (s).

  • 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?

  • signed curvature

    Continuing: "... that has curvature 4 at the origin". Then we should think of the formula for curvature of a curve.

  • Finding Curvature

    109512 Finding Curvature Compute the curvature k(t) of the curve r(t) = 2t i + 4sint j +4cost k Please see the attached file for the complete solution. Thanks for using BrainMass. Curvature is found. The solution is detailed and well presented.

View More Related Solutions