Difference between revisions of "Principle of least reaction"
From Encyclopedia of Mathematics
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A corollary of Gauss' principle (cf. [[Gauss principle|Gauss principle]]), obtained from the latter by using the equations representing Newton's second law for points of a constrained system (see [[#References|[1]]]). According to the principle of least reaction, for the real motion of a system the quantity | A corollary of Gauss' principle (cf. [[Gauss principle|Gauss principle]]), obtained from the latter by using the equations representing Newton's second law for points of a constrained system (see [[#References|[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 | + | 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==== | ====References==== | ||
Latest revision as of 20:17, 11 April 2014
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
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