Hertz principle

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straightest-path principle, principle of least curvature

One of the differential variational principles of classical mechanics, postulated by H. Hertz [1] as the principal law of a mechanics developed by himself. In it, unlike in Newtonian mechanics, the concept of force is replaced by the idea of latent constraints and latent motions. According to Hertz' principle "all free systems remain at rest or in a state of uniform motion along the straightest path" . A free system, according to Hertz, is a system that is not subjected to the action of active forces and is subjected to constraints affecting the mutual locations of the points of the system only; by a straightest path is understood a trajectory each element of which has lesser curvature than any other element with the same initial point and the same tangent to it, and satisfying the constraint equations. The Hertz principle becomes equivalent with the Gauss principle [2] for systems constrained by stationary constraints and not acted upon by active forces.


[1] H. Hertz, "Die Prinzipien der Mechanik" , Gesammelte Werke , 3 , Barth , Leipzig (1894)
[2] N.V. Roze, "Lectures on analytical mechanics" , 1 , Leningrad (1938) (In Russian)



[a1] R.B. Lindsay, H. Margenau, "Foundations of physics" , Dover, reprint (1957)
How to Cite This Entry:
Hertz principle. V.V. Rumyantsev (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098