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1995•Mathematica BohemicaOpen access

Laguerre's differential geometry and kinematics

Zdeněk Jankovský

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Abstract

In this paper the plane Laguerre's geometry in the augmented plane of dual numbers is presented. Basic integral and differential invariants of $\cal L$-curves in the plane are deduced, i.e. the $\cal L$-curve arc, $\cal L$-curvature, $\cal L$-minimal curves, $\cal L$-circle. Furthermore the contact of $\cal L$-curves, $\cal L$-osculating circle, $\cal L$-evolute of a curve and some special $\cal L$-motions are studied from the point of view of $\cal L$-Differential geometry.

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What this paper is about

In this paper the plane Laguerre's geometry in the augmented plane of dual numbers is presented. Basic integral and differential invariants of $\cal L$-curves in the plane are deduced, i.e. the $\cal L$-curve arc, $\cal L$-curvature, $\cal L$-minimal curves, $\cal L$-circle. Furthermore the contact of $\cal L$-curves, $\cal L$-osculating circle, $\cal L$-evolute of a curve and some special $\cal L$-motions are studied from the point of view of $\cal L$-Differential geometry.

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Available abstract

In this paper the plane Laguerre's geometry in the augmented plane of dual numbers is presented. Basic integral and differential invariants of $\cal L$-curves in the plane are deduced, i.e. the $\cal L$-curve arc, $\cal L$-curvature, $\cal L$-minimal curves, $\cal L$-circle. Furthermore the contact of $\cal L$-curves, $\cal L$-osculating circle, $\cal L$-evolute of a curve and some special $\cal L$-motions are studied from the point of view of $\cal L$-Differential geometry.

Key concepts: Osculating circle, Geometry, Plane curve, Differential geometry of curves, Differential geometry, Mathematics, Curvature, Differential (mechanical device)

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