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François Jacques Dominique Massieu (August 4th 1832, Vatteville (Seine-Lower) - February 5th 1896 (Paris)) is a Mathématicien and Physicien French.

Polytechnicien (X1851 promotion), Body of the Mines. Raise with the École des Mines August 1853 in March 1856, left 6th (and the last of its promotion). Established in the body of the mines the 1/10/1857.

Biography

See the very complete site Files of X - Massieu

Work

It made two important theses:

First thesis

The first of these remarkable theses is relating to the algebraic Intégrale S which one frequently meets in the problems of Mécanique for which there exists a function of the forces. Resuming a study already made in 1857 per Mr. Joseph Bertrand, but in which this scientist had restricted himself to examine the movement of a point in a plan, Massieu considers the question from a more general point of view. It first of all sticks to seek the index properties of the algebraic and whole integrals compared to the components speeds, then it establishes several principles with the help of which it simplifies much the examination of the particular cases. It arrives thus, without too tiresome calculations, to find all the Intégrale S Linéaire S and Quadratique S which can admit the problem of the movement of a point free in space or fixed to remain on a given surface.

Among the results of its study, it is two which acquired established among in the science and to which its name remained attached:

1° So that there is an integral of the first degree in the movement of a point on a surface, it is necessary and it is enough that this surface is developable on a surface of revolution;

2° So that there is an integral of the second degree in the movement of a point on a surface, it is necessary and it is enough that this surface has its reducible linear element with the form of Liouville.

These two theorems are of an major importance in the theory of the geodetic lines and were used as starting point with various work.

Second thesis

In its second thesis, Massieu attacks the double refraction, one of the questions of mathematical physics of which erudite world was occupied the then.

In spite of work of Fresnel, of Cauchy, Lamé, one had only incomplete or imperfect theories, resting all on a certain number of assumptions. Massieu makes only one assumption: it consists in extending to the birefringent mediums this fact, shown in experiments for the mediums Monoréfringent S, of the not-interference of the polarized Rayons with right angle.

While being based on this single assumption and making use of the Method of Mac Cullagh to which it gives great developments, the author establishes in a very elegant way surface of the elementary Onde, i.e. envelope of all the plane waves started from the same point in all the directions. This equation quite naturally leads it to the properties of the axes Optique S and the axes of conical Réfraction.

See too

Formula of Massieu

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