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Chetaev principle

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A variational-differential principle of mechanics, a modification of the Gauss principle, established by N.G. Chetaev [1].

According to Chetaev's principle, the work on an elementary cycle, consisting of a direct motion in a fixed force field and an inverse (backward) motion in the force field, that would be sufficient for the creation of a real motion if the mechanical system were completely free, takes a relative (or global) maximum for the real motion in the class of all possible Gaussian motions. Chetaev's principle extends to physical systems and also to continuous media (cf. [2]).

For some more details cf. Variational principles of classical mechanics.

References

[1] N.G. Chetaev, "Modification of the Gauss principle" Prikl. Mat. i Mekh. , 5 : 1 (1941) pp. 11–12 (In Russian)
[2] V.V. Rumyantsev, "On the Chetaev principle" Dokl. Akad. Nauk SSSR , 210 : 4 (1973) pp. 787–790 (In Russian)
How to Cite This Entry:
Chetaev principle. V.V. Rumyantsev (originator), Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Chetaev_principle&oldid=11917
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098