Abstract
It is shown that, to any change of variables:q i=qi(rα, t) (i=1,..., n; α=1,...,n+m; m≦n) increasing the number of variables, it is possible to associate a Mathieu's transformation and conversely. The results are applied to the theory of the osculating plane of motion.
Resumé
On montre qu'à toute transformation:q i=qi(rα, t)(i=1,..., n; α=1,...,n+m; m≦n) augmentant le nombre de variables, on peut associer une transformation de Mathieu et réciproquement. Les résultats sont appliqués à la théorie du plan osculateur du mouvement.
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Pascal, M. A note on the correspondence between Mathieu's transformations and redundant variables in lagrangian mechanics. Celestial Mechanics 24, 53–61 (1981). https://doi.org/10.1007/BF01228793
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DOI: https://doi.org/10.1007/BF01228793