"Advances in theoretical mechanics, bearing on the integration and the alteration in form of dynamical equations, were made since Lagrange by Poisson, William Rowan Hamilton, Jacobi, Madame Kowalevski, and others. Lagrange had established the "Lagrangian form" of the equations of motion. He had given a theory of the variation of the arbitrary constants which, however, turned out to be less fruitful in results than a theory advanced by Poisson. ...Hamilton's method of integration was freed by Jacobi of an unnecessary complication, and was then applied by him to the determination of a geodetic line on the general ellipsoid. With aid of elliptic coordinates Jacobi integrated the partial differential equation and expressed the equation of the geodetic in form of a relation between two Abelian integrals. Jacobi applied to differential equations of dynamics the theory of the ultimate multiplier. The differential equations of dynamics are only one of the classes of differential equations considered by Jacobi. Dynamic investigations along the lines of Lagrange, Hamilton, and Jacobi were made by Liouville, A. Desboves, Serret, J. C. F. Sturm, Ostrogradsky, J. Bertrand, Donkin, Brioschi, leading up to the development of the theory of a system of canonical integrals."