Ñóáêâàíòîâàÿ õðîíîäèíàìèêà

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– 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,

(I.2.8)

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.

(I.2.9)

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.

(I.2.10)

Ìåõàíèêà â ïðîñòðàíñòâå 2O. Ãèïåðñôåðà: UU = 1, ðàçìåðíîñòü 16. Ñòàòè÷íîñòü: (UU) = 0. ßäðî ?U. Îïåðàòîðíûé òåðì (ñì. òàá. 2O):

?’,

(I.2.11)

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,

(I.2.12)

ãäå ?’’, ?, ?, ? – êîíñòàíòû, M, ? – ôóíêöèè ìîìåíòà è ìîìåíòà ñèëû.

Ñèñòåìà äèôôåðåíöèàëüíûõ óðàâíåíèé: (I.2.13)

,

.

?,

,

.

,

,

.

,

,

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