?????? ?????

?????? ????? ????? ??? ??????? ?????? ???????? ??????? ???? ???? ?? ????? ???????? ???? ??????? ?? ?? ????? ????????. ????? ?????? ???????? ?? ????? ?? ???? ??? ????? ??? ???? ?? ???????? ??????? (????????? ?? ????? invariant) ??????? ????? .

?? ?????? ???? ?? ??? ??????? ?? ????? ?? ??? ????? ????? ???? ??? ????? ???????? ?????? ?? ???? ??? ??? ?? ????? ???? ??????? ?????? ??? ?? ???? ????? ???? ??????? ???? ??? ?????? ??? ?? ?????? ??????? (???? ??? ???? ?? ????? ?????? ???? ?? ???????? ?? ????? ?????).

??? ?????? ?????? ????????? ????? ??????? ????? ??????? ??? ?? ?? ????? ?????? ????? ????? ????? ??????? ?? ????? ??? ?????. ^[1] ??????? ???????? ?? ??? ????? ????????? ?????? ???? ????? ?? ??? 1915 ????? ?? ??? 1918? ^[2] ??? ??? ?? ????? ???? ???? ?? ??? ????? ????? ???????? ????? ?? ??? 1909. ^[3] ??? ?????? ????????? ?? ??????? ?????? ????? ?????????? (???? ?? ???? ??????? ?????? ????? ????? ??????????)? ????? ???? ?? ????? ????? ???? ?????? ?? ???? ???? ????? ??????. ????? ??? ???????? ??? ??? ????????? ???????? ??????? ??? ????? ?????.

??????? ?????? ????? ?? ???????? ??????? ?????? ?? ???? ?????????. ???? ??????? ???????? ??? ????? ?????? ?? ???????? ??????? ????????? ??????? (?????? ?????? ?? ???? 1788 ?1833 ??? ???????). ?? ????? ??? ??????? ???? ?? ???? ??????? ???????? ?????????? ??? (??? ???? ??????? ??????? ???? ??? ???? ???? ?????). ???? ???? ???????? ??? ?? ??????? ?? ???? ??????? ???????? ??? ??????? ??????? ????? ??? ?????.

??? ?????? ????? ?????? ??? ?? ??? ????? ????? ???? ?? ????? ???. ??? ???? ??????? ??? ??? ???? ????? ???????? ???? ??? ?????? ?????? ??? ??? ?????? ???? ??? ?????? ?? ?? ?????? ?? ??? ????? ?????? ???? ???????? ?????. ???? ?????? ???????? ?? ?????.

?????? [ ??? ]

???? ?????? ????? ?? ??? 1918 ??? ???? ?? ???? ?????? ???????? ????? ??? ???? ????? ?????? Principle of least action? ??? ???? ???? ???????? ???? ????? ? ???? ???? ?? ?????? ????? ??????? .

?????? ????? ???? ????? ?? ?????????? ??? ????? ????????? ????????? ? ??? ??? ????? ???????? ????? ???? ?? ???? ?? ???? ?? ????????? ?????????? ?????? ???? ??????? ?????? ???? ?? ?????? ??? ????? ????? ?????? ?????? ?? ???? ???? ????? ?????????. ??? ??????? ????????? ???? ???? ?????? ???? ?? ??????? ???????? ? ??? ????? ????????? ???????? ????? ?????? ???????? (??? ?????? ????????? (???? ??????) ????? ????? ??????? ).

????? ???????? ?????? [ ??? ]

??????? ??? ??? ?????? ????????? ???? ???? ??????? ???? ????? ?? ?????? ?? ??????? ??? ???????????? ?? ???? ???????? ?? ?? ????? ?????: ?? ???? ??? ???????? ???? ?????? ????? ?? ????? ?????? ?????? ???? ??????? ????? ?????? ?????? ?????? ???????. ?? ???? ?? ???? ?????? ?????? ???? ????????? ???? ???? ??????? ??????? ??????? ?? ?????? ????? ??? ????? ?????? ??? ????? ?? ??? ??????. ?????? ?????? ?? ?????????.

????? ???? ??? ????? ??????? ?????????? ??? ??????? ???? ????? ?? ?????? ?? ??????? ??? ???????????? ??? ?????? ??? ???????? ???????? ?? ?????? ??????? ??????.

????? ?????? ????? ????? ??? ??? ???? ??????? ???? ?????? ???? ????? ??????? ?????? ???? ????? ???????? ????????? ????? ?????? ?????. ???? ???????? ???????? ?????? ??????? ???????? (???????????) ?? ????????? ???????? ?????? ?????????. ???? ?????? ?? ???? ??? ???? ???????? ???? ???? ????? ?????? ?? ???????????? ?? ??? ??????????? ???????? ?? ??? ??? ?????? ?????????. ??????? ?? ??????? ?????? ????? ???????? ????? ??? ?????? X. ???? ?????? ???? ????? ???????????? ???? ????? ??? X ?? ???? ????? ?????. ???? ?????? ?????? ???? ????? ???????????? ?????? ?????? ???? ??????? ????????? ?????? ????? ??? ??? ?????? ??????? ???????.

???? ??? ???? ???????? [ ??? ]

??? ????? ???? ?????? ?????? ??????? ??????? ?? ?????? ??? ???????? ???? ??? ????.

??? ??? ?????? ????? ????? ?????? ????? ????? ?????? ?????? ??? ????? ?? ?????. ^[4]

??? ???? ???? ?????? ?? ????????? ????? ????? ??? ??????? ??? ?? ???:

?? ????? ?? ????? ?????? ???? ?? ????? ??????? ???? ????? ???? ?????.

???? ???? ≪?????≫ ?? ?????? ?????? ???? ???? ???? ??? ??????? ?? ????? ???? ????? ??????? ????????? ???? ????? ????? ??? ?????? ????? ?? ????????? ????? ?????? ?????? ????? ?????. ???? ?? ?????? ?? ????? ????? ????? ???????? ??????? ???????????. ^[5]

???? ????? [ ??? ]

????? [ ??? ]

^ This is sometimes referred to as Noether's first theorem, see Noether's second theorem .
^ Noether? E. (1918). "Invariante Variationsprobleme" . Nachrichten von der Gesellschaft der Wissenschaften zu Gottingen . Mathematisch-Physikalische Klasse. ?. 1918: 235?257. ????? ?? ????? ?? 2019-08-05.
^ Cosserat? E.? Cosserat? F. (1909). Theorie des corps deformables . Paris: Hermann. ????? ?? ????? ?? 2020-01-26.
^ Thompson, W.J. (1994). Angular Momentum: an illustrated guide to rotational symmetries for physical systems . Wiley. ?. 1. ?. 5. ISBN : 0-471-55264-X . ????? ?? ????? ?? 2020-01-26.
^ Nina Byers (1998) "E. Noether's Discovery of the Deep Connection Between Symmetries and Conservation Laws" . In Proceedings of a Symposium on the Heritage of Emmy Noether, held on 2?4 December 1996, at the Bar-Ilan University, Israel, Appendix B. ???? ?????? 31 ????? 2017 ??? ???? ??? ??? ???? .

[1] This is sometimes referred to as Noether's first theorem, see Noether's second theorem .

[2] Noether? E. (1918). "Invariante Variationsprobleme" . Nachrichten von der Gesellschaft der Wissenschaften zu Gottingen . Mathematisch-Physikalische Klasse. ?. 1918: 235?257. ????? ?? ????? ?? 2019-08-05.

[3] Cosserat? E.? Cosserat? F. (1909). Theorie des corps deformables . Paris: Hermann. ????? ?? ????? ?? 2020-01-26.

[4] Thompson, W.J. (1994). Angular Momentum: an illustrated guide to rotational symmetries for physical systems . Wiley. ?. 1. ?. 5. ISBN : 0-471-55264-X . ????? ?? ????? ?? 2020-01-26.

[5] Nina Byers (1998) "E. Noether's Discovery of the Deep Connection Between Symmetries and Conservation Laws" . In Proceedings of a Symposium on the Heritage of Emmy Noether, held on 2?4 December 1996, at the Bar-Ilan University, Israel, Appendix B. ???? ?????? 31 ????? 2017 ??? ???? ??? ??? ???? .

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