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3. Sila svetovogo davleniya dlya sfericheskoi chasticy s koefficientom otrazheniya
V dannom paragrafe budet naideno analiticheskoe
vyrazhenie dlya sily svetovogo davleniya, deistvuyushei na sfericheskuyu
chasticu radiusa i koefficientom otrazheniya
.
Soglasno vtoromu zakonu N'yutona sila svetovogo davleniya
opredelitsya kak
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Vyberem v kachestve nachala otscheta tochku O, sovpadayushuyu s centrom
chasticy (v nachal'nyi moment vremeni) i sistemu koordinat tak, kak
pokazano na risunke 5. Togda vyrazhenie
(2) mozhno perepisat' v proekciyah na koordinatnye osi
sleduyushim obrazom:
gde proekcii
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Zdes'
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,
,
- proekcii
izmeneniya impul'sa sistemy fotonov, padayushih na chasticu i
otrazhaemyh poslednei za tot zhe promezhutok vremeni.
Budem polagat', chto izluchenie rasprostranyaetsya vdol' osi , v
vide ploskoi elektromagnitnoi volny.
Rassmotrim process padeniya fotona na ploshadku (smotri
ris.5).
Proekcii izmeneniya impul'sa fotona, pogloshennogo chasticei,
soglasno ris.5, opredelyayutsya sistemoi vyrazhenii
(5):
V sluchae fotona, otrazhennogo ot ploshadki, proekcii izmeneniya impul'sa opredelyayutsya sistemoi (6):
Zdes'
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Sledovatel'no, izmenenie impul'sa, sozdavaemoe sistemoi fotonov,
padayushih na ploshadku za edinicu vremeni s chastotami
i pogloshaemyh poslednei, opredelyaetsya
vyrazheniem:
Zdes'
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Sledovatel'no, soglasno (4) imeem:
Pereidem v sfericheskuyu sistemu koordinat posredstvom zameny vida
Zdes' my uchli, chto
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pri etom
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(12) |
Sledovatel'no, (10) mozhno perepisat' v vide:
Poslednie rezul'taty imeyut mesto blagodarya tomu faktu, chto
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zdes'
Sledovatel'no, sila svetovogo davleniya opredelitsya kak
Ochevidno, chto vyrazhenie (18) soderzhit neizvestnye
parametry ,
,
, kotorye podlezhat
opredeleniyu. Tak, v prilozhenii A predstavleno reshenie zadachi o
vychislenii parametra
. Soglasno (16), (17),
dlya vychisleniya
,
neobhodimo znat'
analiticheskuyu zavisimost'
. Reshenie zadachi o
nahozhdenii dannoi zavisimosti predstavleno v prilozhenii B.
Algoritm vychisleniya ukazannyh integralov i analiticheskie
rezul'taty dlya poslednih predstavleny v prilozhenii S. V itoge
vyrazhenie dlya
s uchetom rezul'tatov prilozhenii A-C prinimaet
vid:
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