Principle of least reaction

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A corollary of Gauss' principle (cf. Gauss principle), obtained from the latter by using the equations representing Newton's second law for points of a constrained system (see [1]). According to the principle of least reaction, for the real motion of a system the quantity

is minimal with respect to all motions conceivable in Gauss' sense. Here are the reactions of the constraints and the masses of the points in the system.


[1] N.G. Chetaev, "Stability of motion" , Moscow (1965) (In Russian)



[a1] R.B. Lindsay, H. Margenau, "Foundations of physics" , Dover, reprint (1957)
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Principle of least reaction. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by V.V. Rumyantsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article