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Laboratoire de mathématiques de Lens, Université d'Artois & École polytechnique, Département humanités et sciences sociales: The equation to the secular inequalities in planetary theory from Lagrange to Poincaré This talk aims at shedding a new light on the intertwining of the various branches of mathematical sciences in the 18th and 19th century. We shall start with a specific mathematization that was given in the 18th century to some mechanical problems. In the 1740s, d'Alembert especially mathematized the small oscillations of a swinging string loaded with two bodies by a linear system of two or three differential equations with constant coefficients. The integration of such a system was based on the mathematization of the physical property that the motion of a swinging string loaded with two bodies can be decomposed into the proper oscillations of two strings, each loaded with a single body. In modern parlance, this procedure is tantamount to computing the eigenvalues of a symmetric matrix, i.e. the roots of its characteristic equation. This mathematization was then generalized by Lagrange to the small oscillations of planets on their orbits. From this point on, the characteristic equation was usually designated as the "equation to the secular inequalities in planetary theory". Over the course of the 19th century, this specific equation supported various analogies between several branches of the mathematical sciences, such as mechanics, astronomy, geometry, elasticity, the theory of light, complex analysis, number theory, group theory, etc. By investigating this specific circulation of knowledge in the long run, we shall shed a new light on both the collective dimensions of scientific activities and the individual creativity of mathematicians such as Cauchy and Poincaré. 
 Tuesday, 9
April 2013 |
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