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Additional resources for On the Pressure Variation of Specific Heat of Liquids (1919)(en)(5s)
15 14 The principle is often called the “Principle of Least Action” because its initial formulations spoke in terms of the action being minimized rather than the more general case of taking on a stationary value. The term “Principle of Least Action” is also commonly used to refer to a result, due to Maupertuis, Euler, and Lagrange, which says that free particles move along paths for which the integral of the kinetic energy is minimized among all paths with the given endpoints. Correspondingly, the term “action” is sometimes used to refer specifically to the integral of the kinetic energy.
These are also fine coordinates, but we will have to explicitly keep in mind the constraints that limit the possible configurations to the actual geometry of the system. Sets of coordinates with the same dimension as the configuration space are easier to work with because we do not have to deal with explicit constraints among the coordinates. So for the time being we will consider only formulations where the number of configuration coordinates is equal to the number of degrees of freedom; later we will learn how to handle systems with redundant coordinates and explicit constraints.
The earliest action principle that remains part of modern physics is Fermat’s Principle, which states that the path traveled by a light ray between two points is the path that takes the least amount of time. Fermat formulated this principle around 1660 and used it to derive the laws of reflection and refraction. Motivated by this, the French mathematician and astronomer Pierre-Louis Moreau de Maupertuis enunciated the Principle of Least Action as a grand unifying principle in physics. ” For a historical perspective of Maupertuis’s, Euler’s, and Lagrange’s roles in the formulation of the principle of least action, see Jourdain .