Displaying similar documents to “On the last geometric statement of Jacobi.”

Generalized geodesic deviations: a Lagrangean approach

R. Kerner (2003)

Banach Center Publications

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The geodesic deviation equations, called also the Jacobi equations, describe only the first-order effects, linear in the small parameter characterizing the deviation from an original worldline. They can be easily generalized if we take into account the higher-order terms. Here we derive these higher-order equations not only directly, but also from the Taylor expansion of the variational principle itself. Then we show how these equations can be used in a novel approach to the two-body...

On Jacobi fields and a canonical connection in sub-Riemannian geometry

Davide Barilari, Luca Rizzi (2017)

Archivum Mathematicum

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In sub-Riemannian geometry the coefficients of the Jacobi equation define curvature-like invariants. We show that these coefficients can be interpreted as the curvature of a canonical Ehresmann connection associated to the metric, first introduced in [15]. We show why this connection is naturally nonlinear, and we discuss some of its properties.

Beyond the edge of certainty : reflections on the rise of physical conventionalism

Helmut Pulte (2000)

Philosophia Scientiae

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Until today, conventionalism is mainly regarded from the point of view of geometry, both in historical as in philosophical perspective. This paper, which corresponds in a certain way with earlier studies of J. Giedymin, aims at a broader interpretation. The importance of the so-called ‘physics of principles’, rooted in the tradition of analytical mechanics, for Poincaré’s conventionalism is emphasized. It is argued that important elements of physical conventionalism can already be found...