Potential motion in a geometric setting: Presenting differential geometry methods in a classical mechanics course

A. A. Deriglazov

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The standard classical mechanics textbooks used at graduate level mention geometrization of the potential motion kinematics. We show that the complete problem can also be geometrized, presenting the system of equations of geometric origin equivalent to the equations of motion of the potential system. The subject seems to be an excellent opportunity for introducing differential geometry concepts already in the classical mechanics course. After presenting the necessary differential geometry notions, the classical mechanical potential system is described in geometric terms. To the system one associates a Riemann space with an appropriately chosen metric and affine connection, both specified by the potential. In this picture, both dynamics and kinematics acquire invariant geometric meaning.

Original languageEnglish
Pages (from-to)767-780
Number of pages14
JournalEuropean Journal of Physics
Volume29
Issue number4
DOIs
Publication statusPublished - 1 Jul 2008

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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