This scientist also names a method for finding the extrema of a constrained function.
With D'Alembert, this scientist names a principle that equates the sum of the total internal and external work along any virtual displacement to zero. He used that principle, which is not restricted to holonomic constraints, to derive equations named after Euler and this scientist without using Hamilton's principle. Those equations equate the position derivative of this scientist's namesake (*) function to the time derivative of the velocity derivative of that namesake function. The calculus of variations is based on that equation, which uses this man's namesake function, which is the difference between kinetic and potential energy. This scientist also names a method for finding the extrema of a constrained function. For 10 points, name this scientist with some namesake multipliers.
With D'Alembert, this scientist names a principle that equates the sum of the total internal and external work along any virtual displacement to zero.
Joseph-Louis Lagrange [accept Giuseppe Lodovico Lagrangia]