# Principle of least reaction

From Encyclopedia of Mathematics

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) |

#### Comments

#### References

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

**How to Cite This Entry:**

Principle of least reaction.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Principle_of_least_reaction&oldid=31557

This article was adapted from an original article by V.V. Rumyantsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article