Abstract
In this note we revisit E. Cartan's address at the 1928 International Congress of Mathematicians at Bologna, Italy. The distributions considered here will be of the same class as those considered by Cartan, a special type which we call strongly or maximally non-holonomic. We set up the groundwork for using Cartan's method of equivalence (a powerful tool for obtaining invariants associated to geometrical objects), to more general non-holonomic distributions.
Highlights
Le vrai problème de la represéntation géométrique d’un système matériel non holonome consiste [· · · ] dans la recherche d’un schéma géométrique lié d’une maniére invariante aux propriétés mécaniques du système
The adapted basis is the dual basis of the ωI
Equations (3.16) should be solved simultaneously with (3.12) and (3.13). This approach can be helpful for setting up numerical methods, and in some cases reducing the non-holonomic system to a second order equation on Rm
Summary
Le vrai problème de la represéntation géométrique d’un système matériel non holonome consiste [· · · ] dans la recherche d’un schéma géométrique lié d’une maniére invariante aux propriétés mécaniques du système. The distributions considered by Cartan were of a special type which we call strongly or maximally non-holonomic. Our aim is to set up the groundwork for using Cartan’s method of equivalence (a powerful tool for obtaining invariants associated to geometrical objects (Gardner 1989) to more general non-holonomic distributions. This is a local study, but we outline some global aspects. Lower case roman characters i, j, k run from 1 to m (representing the constraint distribution).
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