History[edit]
The method of variation of parameters was first sketched by the Swiss mathematician Leonhard Euler (1707–1783), and later completed by the Italian-French mathematician Joseph-Louis Lagrange (1736–1813).[1]
A forerunner of the method of variation of a celestial body's orbital elements appeared in Euler's work in 1748, while he was studying the mutual perturbations of Jupiter and Saturn.[2] In his 1749 study of the motions of the earth, Euler obtained differential equations for the orbital elements.[3] In 1753, he applied the method to his study of the motions of the moon.[4]
Lagrange first used the method in 1766.[5] Between 1778 and 1783, he further developed the method in two series of memoirs: one on variations in the motions of the planets[6] and another on determining the orbit of a comet from three observations.[7] During 1808–1810, Lagrange gave the method of variation of parameters its final form in a third series of papers.[8]