Principle of least reaction

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

$$\sum_\nu\frac{R_\nu^2}{2m_\nu}$$

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

References

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

References

[a1]	R.B. Lindsay, H. Margenau, "Foundations of physics" , Dover, reprint (1957)