– div A – ?? – divp B = 0,
+ grad ? + rot A + ?B – gradp ? – rotp B = 0,
– div B + ?? + divp A = 0,
+ grad ? – rot B – ?A + gradp ? – rotp A = 0,
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(I.2.8)
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ãäå êîíñòàíòû ïðèíÿòû ðàâíûìè 1.
Åñëè ïîòåíöèàëû ?, ?, A, B íå çàâèñÿò îò èìïóëüñíûõ êîîðäèíàò, òî ïîñò’îêòåòíàÿ ñèñòåìà (I.2.8) óïðîùàåòñÿ:
– div A – ?? = 0,
+ grad ? + rot A + ?B = 0,
– div B + ?? = 0,
+ grad ? – rot B – ?A = 0.
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(I.2.9)
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Ïóñòü H = rot A, E = – ?A/?t – grad ?, HB = rot B, EB = – ?B/?t – grad ?, òîãäà â êàëèáðîâêå div A = 0, div B = 0 ïîëó÷èì ñèñòåìó óðàâíåíèé:
??/?t = ??, ?? = 0, ??/?t = – ??, ?? = 0.
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(I.2.10)
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Ìåõàíèêà â ïðîñòðàíñòâå 2O. Ãèïåðñôåðà: UU = 1, ðàçìåðíîñòü 16. Ñòàòè÷íîñòü: (UU) = 0. ßäðî ?U. Îïåðàòîðíûé òåðì (ñì. òàá. 2O):
![](D:/Syte29/qame.ru/book/science/hronodinamika/_%D0%92%D0%B5%D1%80%D0%B5%D1%89%D0%B0%D0%B3%D0%B8%D0%BD%20%D0%98.%D0%90.,%20%D0%A1%D1%83%D0%B1%D0%BA%D0%B2%D0%B0%D0%BD%D1%82%D0%BE%D0%B2%D0%B0%D1%8F%20%D1%85%D1%80%D0%BE%D0%BD%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0/_%D0%92%D0%B5%D1%80%D0%B5%D1%89%D0%B0%D0%B3%D0%B8%D0%BD%20%D0%98.%D0%90.,%20%D0%A1%D1%83%D0%B1%D0%BA%D0%B2%D0%B0%D0%BD%D1%82%D0%BE%D0%B2%D0%B0%D1%8F%20%D1%85%D1%80%D0%BE%D0%BD%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0.126.png)
?’ ,
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(I.2.11)
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ãäå ?’, ?, ?, ? – êîíñòàíòû; – îïåðàòîðû, ïîäîáíûå îïåðàòîðó ?; mx, my, mz – êîìïîíåíòû ìîìåíòà èìïóëüñà; fx, fy, fz – êîìïîíåíòû ìîìåíòà ñèëû. Îïåðàòîð ? – ýòî îáîáùåíèå îïåðàòîðà ? íà 16 èçìåðåíèé.
Ïðåäìåòíûé òåðì â ïðîñòðàíñòâå áèîêòàâ [1, cc. 106 – 115]:
U = uT + ix + jy + kz + m’(?H + ipx + jpy + kpz)E +
+ ?’’[?M + imx + jmy + kmz + m’(?? + ifx + jfy + kfz)E]F,
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(I.2.12)
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ãäå ?’’, ?, ?, ? – êîíñòàíòû, M, ? – ôóíêöèè ìîìåíòà è ìîìåíòà ñèëû.
Ñèñòåìà äèôôåðåíöèàëüíûõ óðàâíåíèé: (I.2.13)
,
.
? ,
,
.
,
,
.
,
,
— 21 —
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