For 10 points, name this French scientist who developed a namesake form of mechanics.
In general relativity, a quantity named for this man is proportional to the square root of the negative of the metric tensor. More generally, the derivative of that quantity with respect to a generalized coordinate appears in an equation named for this man and Euler. In a method named for this man, one sets the gradients of a function and a constraint proportional to one another. In addition to that method of multipliers, he names a set of five points at which a small object orbits in sync with two larger objects, as well as a quantity equal to kinetic energy minus potential energy. For 10 points, name this French scientist who developed a namesake form of mechanics.
In general relativity, a quantity named for this man is proportional to the square root of the negative of the metric tensor.
Joseph-Louis Lagrange