Mechanics, volume 2
Mechanica (this volume, along with E15) is Euler's outline of a program of studies embracing every branch of science, involving a systematic application of analysis. It laid the foundations of analytical mechanics, the result of Euler's consideration of the motion produced by forces acting on both free and constrained points. It was also the first published work in which the number e appeared. In this volume, Euler considers motion of a point-mass lying on a given curve or surface. He derives some differential equations of the geodesics governing the problem of free motion on a surface. In this way, he shows that the path of a mass-point that is free to move on a fixed surface is locally the shortest possible path between its initial and final points.
Original Source Citation
St. Petersburg: Imperial Academy of Sciences, Volume 2, pp. 1-500.
Opera Omnia Citation
Series 2, Volume 2, pp.1-459.