Application of the geometry of curves in Euclidean space | Zendy

Kostadin Trenčevski | Zendy

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Application of the geometry of curves in Euclidean space

Author(s) -

Kostadin Trenčevski

Publication year - 2019

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1904029t

Subject(s) - mathematics , lorentz transformation , galilean , geometry , differential geometry of curves , inertial frame of reference , euclidean space , spin (aerodynamics) , torsion (gastropod) , curvature , euclidean geometry , galilean transformation , mathematical analysis , minkowski space , space (punctuation) , classical mechanics , mathematical physics , physics , medicine , differential algebraic equation , ordinary differential equation , linguistics , surgery , philosophy , thermodynamics , differential equation

In this article the so called induced spin velocities are studied, and it is an improvement of the paper [13] using the geometry of curves in 3-dimensional Euclidean space. Some essential properties of them are given, and they are rather different than the ordinary velocities. Indeed, the induced spin velocities are non-inertial and instead of the Lorentz transformations for them the Galilean transformations should be used. The induced spin velocity is derived in terms of the curvature and torsion of the trajectory. Two applications of the induced spin velocities are studied.

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