B-SKOBbLfl B03MyiHEHIfl CEMH EO.H.inHXT> n.IAUETl». (9) 345 



noKaswBaiOTT), 4to c, c, c" cyTB npo.iojKemfi Ha ii.iockocth op4HHaTT> XY, XZ n YZ 4BOHHaro 

 Bbip-fesKa q, onnci»iBaeMaro pa4iycoM r B-BeKTopoMt ua iuiockocth opÔHTW bt> e4ninmy BpeMeriH. 



6. Kt> nepBUM'B nirrerpa.iaMT> ypaBHeniii sjbiHnTHqecKaro 4BH>KeHifl npHHa^eacaT'B 

 ypaBnema 



(d^-i-^î/) 2 -!-^ 2(A _ „, xdy—ydx 



(d<) 2 r ' dt ' 



IlHTerpa.ibi ypaBHeuin B03Mymaemaro 3Ji.ninTnqecKaro 4BH>Keui>i 6y&yTb hm'Btb tott> ace 

 caMbiîi bh4t>, Kor4a npHMeM'B, hto mwhasaoTcn npoH3BOJbHbia nocTofliiHbifl h n c, t. e. nor4a 

 nojiOîKHM'b (0t4. ï, ht. 2) 



dh = ~ dx -t— *— dy -+-^-dz== (dR) , 



dx dy J dz v ; 



dc ={ x T y -yf x ) dL 



Ho KaKi. Koop4iinaTbi x, y, z cyTb o>yHKu,iio yr^ra nt -+- t, to 



dh == - nd* = n*^ dt, 



ndt dz 

 T4'B n CIHTaeTCfl KOTHHeCTOIH'b nOCTOflHHblMX. 



HîOîK'b KacaeTCH 40 BToparo ypaBHema, to 3aniT>THM'b , hto N, KaKT> 4>yHKujji op4HnaTb 

 x, y, 4aerb 



dR dR dx dR dy 



dN lx'dN~*~ly'dN 1 



r4'fe, no <i>opMyTaMT> npeo6pa30Bauia Koop4HHarb H.ieHa 5, 



dx dy 



dN~ ~y'dN~ X ' 



h noTOMy 



, dR dR \ , dR , 



dc =(dy œ --dxy) dt = dN fU ^ 



t. e. HacTHbiii 4H<i>*epeHma.n> 



dN 



eCTB MOM6HTT> B03MymaK)HHJX r b OMIT, Ha nTOCKOCTH XY H OKO.TO OCH 2-BT> , nOMHOÎKetlHblH Ha 



3je»ieHTT> BpesieHH dl. Ho KaKT» yrorb [3 a BbipisoE/b q HaxoTflTcn Ha n.iocKOCTH op6iiTi>i, 



TO MOMeHTT> BO3Mymai0mHX , b CH.IT> Ha 3TOH n.IOCKOCTH H OKO.IO OCH s'-BX 6y4CTT. 



dR . , 



T$ dt = d( l- 



^.aaie : MOMeHTT> BOSMymaioiHHXT. chtt> Ha nTOCKocTn yrja / ecTb ~~. Ec.ih npo.ioHte- 

 me 94e»ieHTa dq na 3Ty n.iocicocTb H3o6pa3HMT> Hpe3T> dg; to no.iyHHMT> 



dg = '£dt. 



OcTaeTca onpe4 r fe.iHTi> dg. J{ar 3Toro BcnoMHHMT>, hto ecin Kaicafl nn6)4b n.ioma4b npojojKena 

 Ha Tpn nTOCKocTH Koop4iiHaT r b, to en npo.iOHieuie ua BcaKyio njocnocTb, npox<»4>iiuyio Hpeai. 



Mém. se. math, et phys. T. VII. 44 



