Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



From a dynamical system of the knee to natural jet geometrical objects

Authors: Mircea Neagu and Mihaela Maria Marin
Journal: Quart. Appl. Math. 71 (2013), 689-705
MSC (2000): Primary 58A20, 53C07; Secondary 53C43, 83C22
DOI: https://doi.org/10.1090/S0033-569X-2013-01307-4
Published electronically: September 5, 2013
MathSciNet review: 3136991
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we construct some natural geometrical objects on the $ 1$-jet space $ J^{1}(\mathbb{R},\mathbb{R}^{3})$, like a nonlinear connection, a Cartan linear connection (together with its d-torsions and d-curvatures), a jet ``electromagnetic" d-field and its geometric ``electromagnetic" Yang-Mills energy, starting from a given dynamical system governing the three-dimensional motion of the knee in the mathematical model introduced by Grood and Suntay. The computer-drawn graphics of corresponding Yang-Mills energetic surfaces of constant level (produced by this knee dynamical system) are given.

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Additional Information

Mircea Neagu
Address at time of publication: University Transilvania of Braşov, Department of Mathematics-Informatics, Blvd. Iuliu Maniu, no. 50, Braşov 500091, Romania.
Email: mircea.neagu@unitbv.ro

Mihaela Maria Marin
Address at time of publication: University Transilvania of Braşov, Faculty of Mechanical Engineering, Str. Politehnicii, no. 1, Braşov 500024, Romania
Email: marin_mihaela_maria@yahoo.com

DOI: https://doi.org/10.1090/S0033-569X-2013-01307-4
Keywords: 1-jet spaces, dynamical system of knee, jet least squares Lagrangian function, jet single-time Lagrange geometry, ``electromagnetic'' Yang-Mills energy.
Received by editor(s): November 16, 2011
Published electronically: September 5, 2013
Article copyright: © Copyright 2013 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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