* Pierre-Simon Laplace publishes Exposition du système du monde, his work on astronomy ( mainly celestial mechanics ) following Newton and Lagrange.

* Lagrange publishes a paper on the stability of planetary orbits.

* Lagrange publishes his Résolution des équations numériques, including the method of approximating to the real roots of an equation by means of continued fractions.

* Lagrange publishes his Théorie des fonctions analytiques.

* Lagrange publishes a paper on the motion of the nodes of a planet's orbit.

* Lagrange discusses representations of integers by general algebraic forms ; produces a tract on elimination theory ; publishes his first paper on the general process for solving an algebraic equation of any degree via Lagrange resolvents ; and proves Bachet's theorem that every positive integer is the sum of four squares.

* Lagrange publishes on the libration of the Moon, and an explanation as to why the same face is always turned to the Earth, a problem which he treats with the aid of virtual work, containing the germ of his idea of generalized equations of motion.

Not all of the ring material would have necessarily been swept up right away ; the thickened crust of the Far Side suggests that a second moon about 1, 000-km in diameter formed in a Lagrange point of the Moon ; after tens of millions of years, as the two moons migrated outward from the Earth, solar tidal effects would have made the Lagrange orbit unstable, resulting in a slow-velocity collision that would have ' pancaked ' the smaller moon onto what is now the Far Side.

In classical mechanics, the equation of motion is Newton's second law, and equivalent formulations are the Euler – Lagrange equations and Hamilton's equations.

In this instance, sometimes the term refers to the differential equations that the system satisfies ( e. g., Newton's second law or Euler – Lagrange equations ), and sometimes to the solutions to those equations.

These were developed intensively from the second half of the eighteenth century ( by, for example, D ' Alembert, Euler, and Lagrange ) until the 1930s.

This is a generalization of the Euler – Lagrange equation: indeed, the functional derivative was introduced in physics within the derivation of the Lagrange equation of the second kind from the principle of least action in Lagrangian mechanics ( 18th century ).

Since the Lagrangian ( eq ( 1 )) contains second derivatives, the Euler – Lagrange equation of motion for this field is

In 1933 he met his second wife, actress Louise Lagrange ( 1898-1979 ), while shooting his film, L ' Homme mystérieux.

Château Lagrange produces three wines ; an eponymous grand vin ( about 23, 000 cases ), a second wine called Les Fiefs de Lagrange ( about 31, 000 cases ), and since 1997, a small amount of white wine called Les Arums de Lagrange.

A further step was the 1770 paper Réflexions sur la résolution algébrique des équations by the French-Italian mathematician Joseph Louis Lagrange, in his method of Lagrange resolvents, where he analyzed Cardano and Ferrarri's solution of cubics and quartics by considering them in terms of permutations of the roots, which yielded an auxiliary polynomial of lower degree, providing a unified understanding of the solutions and laying the groundwork for group theory and Galois theory.

* Lagrange submits a paper on the movements of Jupiter's satellites to the Académie française.

The Medford Cutoff from Packard to South Lagrange was completed in 1907 ; and a branch was built from Millinocket to a new paper mill in East Millinocket.

He had also intervened on behalf of a number of foreign-born scientists including mathematician Joseph Louis Lagrange, granting them exception to a mandate stripping all foreigners of possessions and freedom .< ref >

At 15, he was reading the original papers of Joseph Louis Lagrange, such as the landmark Réflexions sur la résolution algébrique des équations which likely motivated his later work on equation theory, and Leçons sur le calcul des fonctions, work intended for professional mathematicians, yet his classwork remained uninspired, and his teachers accused him of affecting ambition and originality in a negative way.

In the distant future, Mankind has colonized space ( with clusters of space colonies at each of the five Earth-Moon Lagrange points ), and, down on the Earth, the nations have united as the United Earth Sphere Alliance.

Joseph Louis Lagrange was an admirer of Euler and, in his work on integrating probability density functions, investigated expressions of the form

The general theory of Pell's equation, based on continued fractions and algebraic manipulations with numbers of the form was developed by Lagrange in 1766 – 1769.

With the later development of abstract groups, this result of Lagrange on polynomials was recognized to extend to the general theorem about finite groups which now bears his name.

Within two years and a half he had mastered all the subjects prescribed for examination, and a great deal more, and, on going up for examination at Toulouse, he astounded his examiner by his knowledge of J. L. Lagrange.

Yet, an explicit expression of the error was provided much later on by Joseph-Louis Lagrange.

The key advantage of a linear penalty function is that the slack variables vanish from the dual problem, with the constant C appearing only as an additional constraint on the Lagrange multipliers.

As a result of surface area minimization, a surface will assume the smoothest shape it can ( mathematical proof that " smooth " shapes minimize surface area relies on use of the Euler – Lagrange equation ).

A post office was established on January 9, 1867, with Bryant S. Lagrange as the first postmaster.

Now, for any N, because of the Euler – Lagrange theorem, on shell ( and only on-shell ), we have

Thus, the force on a particle due to a scalar potential,, can be interpreted as a Lagrange multiplier determining the change in action ( transfer of potential to kinetic energy ) following a variation in the particle's constrained trajectory.

We use Lagrange multipliers to find the point of maximum entropy,, across all discrete probability distributions on.

* Lagrange multipliers on Banach spaces: another generalization of the method of Lagrange multipliers.

* MIT Video Lecture on Lagrange Multipliers

* Slides accompanying Bertsekas's nonlinear optimization text, with details on Lagrange multipliers ( lectures 11 and 12 )

After releasing the sample return capsule on September 8, 2004, the spacecraft bus traveled back toward the Earth-Sun Lagrange Point ( L1 ).

Locations where the ribbon changes direction abruptly represent trajectory changes at Lagrange points, while constricted areas represent locations where objects linger in temporary orbit around a point before continuing on

Launched in 1978, the ISEE-3 spacecraft was sent on a mission to orbit around one of the Lagrange points.

Weakened by serious health problems, Tati died on 4 November 1982, of a pulmonary embolism, leaving a final scenario called Confusion that he had completed with Jacques Lagrange.

To this journal, at the age of twenty, Cayley contributed three papers, on subjects which had been suggested by reading the Mécanique analytique of Lagrange and some of the works of Laplace.

This theorem was proven by Joseph Louis Lagrange in 1770, and corresponds to Fermat's theorem on sums of two squares.

* " Home on Lagrange ( The L5 Song )", a filk song