Understanding Torsion of Curve: Normal Unit Vector Explanation

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Torsion of a curve is understood as the measure of how much the curve twists out of the plane formed by the tangent and normal unit vectors. The Frenet-Serret formulas provide a mathematical framework for analyzing space curves, starting with the tangent vector derived from the curve's functional definition. This system generates two additional orthogonal vectors, creating a co-moving orthogonal reference frame. The discussion emphasizes the relevance of these concepts in vector calculus and their applications in various engineering fields. Understanding these principles is crucial for analyzing the geometric properties of curves.
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how can we understand torsion of curve is in the direction of normal unit vector en?
 

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It is a mathematical system which helps with space curves; it starts with the idea that the tangent to a curve can be found by taking the derivative of the curve's functional definition wrt the distance along the curve.

Then two more orthogonal vectors are created, providing a co-moving orthogonal reference system.

This is usually first encountered in a vector calculus course, though it is useful in many areas of engineering.
 

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