It happens to be that this Italian gentleman revolutionized the world of Physics some two hundred years ago (see here a beautiful explanation on how), in such a manner that now is nearly impossible not to encounter his surname nearly everywhere when trying to understand them.
The following is a short outline of the mathematical/physical concepts including Lagrange (a larger version can be found in http://en.wikipedia.org/wiki/List_of_topics_named_after_Joseph_Louis_Lagrange):
- Lagrange multipliers: These are mathematical artifacts for the solution of optimization problems (http://en.wikipedia.org/wiki/Lagrange_multiplier)
- Euler-Lagrange equation: The Euler–Lagrange equation was developed in the 1750s by Euler and Lagrange in connection with their studies of the tautochrone
problem. This is the problem of determining a curve on which a weighted
particle will fall to a fixed point in a fixed amount of time,
independent of the starting point. Lagrange solved this problem in 1755 and sent the solution to Euler.
The two further developed Lagrange's method and applied it to mechanics, which led to the formulation of Lagrangian mechanics.
- Lagrangian function: The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics by Irish mathematician William Rowan Hamilton known as Lagrangian mechanics.
- Green-Lagrangian tensor: In continuum mechanics, the finite strain theory also called large strain theory, or large deformation theory, deals with deformations in which both rotations and strains are arbitrarily large. This means to invalidate the assumptions inherent in infinitesimal strain theory. In this case, the undeformed and deformed configurations of the continuum are significantly different and a clear distinction has to be made between them. This is commonly the case with elastomers, plastically-deforming materials and other fluids and biological soft tissue. The concept of strain is used to evaluate how much a given displacement differs locally from a rigid body displacement . One of such strains for large deformations is the Lagrangian finite strain tensor, also called the Green-Lagrangian strain tensor or Green - St-Venant strain tensor.
Eulerian description Lagrangian description
It must be said that Lagrange's prolificacy results somehow dazing and stunning, as there are so many fields he got involved in, and none of them of trivial nature.
I hope this quick outline serves others to find a way through all this tangled knowledge.