A pair of kinematically related space curves

Title

A pair of kinematically related space curves

Creator

Bhat V.S.; Haribaskar R.

Description

We investigate the relation between two types of space curves, the Mannheim curves and constant-pitch curves and primarily explicate a method of deriving Mannheim curves and constant-pitch curves from each other by means of a suitable deformation of a space curve. We define a "radius" function and a "pitch" function for any arbitrary regular space curve and use these to characterize the two classes of curves. A few non-trivial examples of both Mannheim and constant pitch curves are discussed. The geometric nature of Mannheim curves is established by using the notion of osculating helices. The Frenet-Serret motion of a rigid body in theoretical kinematics is studied for the special case of a Mannheim curve and the axodes in this case are deduced. In particular, we show that the fixed axode is developable if and only if the motion trajectory is a Mannheim curve. 2018 World Scientific Publishing Company.

Source

International Journal of Geometric Methods in Modern Physics, Vol-15, No. 10

Date

2018-01-01

Publisher

World Scientific Publishing Co. Pte Ltd

Subject

Axode; constant pitch; Frenet-Serret motion; Mannheim curve; moving frame; pitch

Coverage

Bhat V.S., Department of Mathematics, Christ University, Hosur Road, Bangalore, Karnataka, 560078, India; Haribaskar R., Department of Mathematics, Christ University, Hosur Road, Bangalore, Karnataka, 560078, India

Rights

Restricted Access

Relation

ISSN: 2198878

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.1142/S0219887818501803

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