An Alternative Approach to Find the Position Vector of a General Helix

Abstract

In this paper, we introduce an alternative approach centered around an alternative moving frame for finding the position vector of a general helix given its curvature and torsion. Our methodology begins by formulating a vector differential equation, leveraging the unit principal normal vector of a general helix with the assistance of the alternative moving frame. Then, by solving this differential equation, we obtain the position vector of the general helix. This innovative technique is then applied to ascertain the position vector of a circular helix. To illustrate the effectiveness of our method, we showcase parametric representations of various general helices, each defined by unique curvature and torsion functions.

Keywords

• Alternative moving frame
• curvatures
• general helix
• position vector

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