Добавил:
Upload
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз:
Предмет:
Файл:4 семестр (2 курс)лала / Физика / Кратко / 11 Временное и стационарное ур
.txt яю1 1 . @5<5==>5 8 AB0F8>=0@=>5 C@02=5=8O (@548=35@0. !B0F8>=0@=K5 A>AB>O=8O. 20=B>20=85 M=5@388.
#@02=5=85 (@Q48=35@0 >?8AK205B 87<5=5=85 2> 2@5<5=8 A>AB>O=8O :20=B>2>3> >1J5:B0, E0@0:B5@87C5<>3> 2>;=>2>9 DC=:F859.
2@5<5==>5 ( =5AB0F8>=0@=>5) C@02=5=85 (@Q48=35@0: i * h ( A G5@B>9) * [ G0AB=0O ?@>872>4=0O] ! ?> t = - ( h ( A G5@B>9) ^ 2 / 2 * m ) [ B@5C3>;L=8:, 2 C3;0 2=87C, 1 225@EC] !+ U * !, [ B@5C3>;L=8:] - >?5@0B>@ 0?;0A0.
!B0F8>=0@=K<8 A>AB>O=8O<8 =07K20NB A>AB>O=8O, 2 :>B>@KE 2A5 =01;N405<K5 D878G5A:85 25;8G8=K =5 87<5=ONBAO A B5G5=85< 2@5<5=8. G0AB=>AB8, =5 87<5=O5BAO A> 2@5<5=5< ?;>B=>ABL 25@>OB=>AB8 !( [ 25:B>@] r , t ) ^ 2 . !B0F8>=0@=K5 @5H5=8O C@02=5=8O (@Q48=35@0 8<5NB A<KA; 4;O B5E 7040G, 2 :>B>@KE A8;>2>5 ?>;5 ?>B5=F80;L=> 8, A;54>20B5;L=>, ?>B5=F80;L=0O M=5@38O U =5 7028A8B >B 2@5<5=8: U = U ( x , y , z ) .
AB0F8>=0@=KE A>AB>O=8OE A>AB>O=85 G0AB8FK 2 40==K9 <><5=B 2@5<5=8 >?8AK205BAO ?5@8>48G5A:>9 DC=:F859 2@5<5=8 ! A F8:;8G5A:>9 G0AB>B>9 w ( ><M30) . @8 MB>< !- DC=:F8O >?@545;O5BAO ?>;=>9 M=5@3859 G0AB8FK.
!B0F8>=0@=>5 C@02=5=85 (@Q48=35@0: [ B@5C3>;L=8:] ?A8( <0;5=L:>5) + ( 2 * m / h ( A G5@B>9) ^ 2 ) * ( E - U ) * ?A8( <0;5=L:>5) = 0 .
20=B>20=85 M=5@388. #GB5<, GB> D878G5A:89 A<KA; 8<5NB ;8HL B0:85 @5H5=8O C@02=5=8O( BCB 8 40;55 3>2>@8BAO ?@> AB0F8>=0@=>5) , :>340 =52@5<5==0O 2>;=>20O DC=:F8O ?A8( <0;5=L:>5) ( [ 25:B>@] r ) 8 55 ?5@2K5 ?@>872>4=K5 ?> :>>@48=0B0< C4>2;5B2>@ONB AB0=40@B=K< CA;>28O<. -B8 CA;>28O O2;ONBAO B@51>20=8O<8, =0:;04K205<K<8 =0 8A:><>5 @5H5=85 48DD5@5=F80;L=>3> C@02=5=8O. 5H5=8O C@02=5=8O (@Q48=35@0, C4>2;5B2>@ONI85 MB8< CA;>28O<, >:07K20NBAO 2>7<>6=K<8 ;8HL ?@8 =5:>B>@KE 7=0G5=8OE M=5@388 , =07K205<KE A>1AB25==K<8 7=0G5=8O<8 M=5@388. $C=:F88 ?A8, O2;ONI85AO @5H5=8O<8 C@02=5=8O ?@8 MB8E 7=0G5=8OE M=5@388, =07K20NBAO A>1AB25==K<8 DC=:F8O<8, ?@8=04;560I8<8 A>1AB25==K< 7=0G5=8O< .
!>1AB25==K5 7=0G5=8O <>3CB >1@07>2K20BL :0: =5?@5@K2=K9, B0: 8 48A:@5B=K9 @O4. ?5@2>< A;CG05 3>2>@OB > =5?@5@K2=>< ( A?;>H=><) A?5:B@5 M=5@388, 2> 2B>@>< > 55 48A:@5B=>< A?5:B@5.
#@02=5=85 (@Q48=35@0 O2;O5BAO <0B5<0B8G5A:8< 2K@065=85< :>@?CA:C;O@=>- 2>;=>2>3> 4C0;87<0. => C4>2;5B2>@O5B ?@8=F8?C A>>B25BAB28O >@0 8 2 ?@545;L=>< A;CG05, :>340 4;8=0 2>;=K 45 @>9;O 7=0G8B5;L=> <5=LH5 @07<5@>2, E0@0:B5@=KE 4;O @0AA<0B@8205<>3> 42865=8O, ?>72>;O5B >?8A0BL 42865=85 G0AB8F ?> 70:>=0< :;0AA8G5A:>9 <5E0=8:8.
#@02=5=85 (@Q48=35@0 >?8AK205B 87<5=5=85 2> 2@5<5=8 A>AB>O=8O :20=B>2>3> >1J5:B0, E0@0:B5@87C5<>3> 2>;=>2>9 DC=:F859.
2@5<5==>5 ( =5AB0F8>=0@=>5) C@02=5=85 (@Q48=35@0: i * h ( A G5@B>9) * [ G0AB=0O ?@>872>4=0O] ! ?> t = - ( h ( A G5@B>9) ^ 2 / 2 * m ) [ B@5C3>;L=8:, 2 C3;0 2=87C, 1 225@EC] !+ U * !, [ B@5C3>;L=8:] - >?5@0B>@ 0?;0A0.
!B0F8>=0@=K<8 A>AB>O=8O<8 =07K20NB A>AB>O=8O, 2 :>B>@KE 2A5 =01;N405<K5 D878G5A:85 25;8G8=K =5 87<5=ONBAO A B5G5=85< 2@5<5=8. G0AB=>AB8, =5 87<5=O5BAO A> 2@5<5=5< ?;>B=>ABL 25@>OB=>AB8 !( [ 25:B>@] r , t ) ^ 2 . !B0F8>=0@=K5 @5H5=8O C@02=5=8O (@Q48=35@0 8<5NB A<KA; 4;O B5E 7040G, 2 :>B>@KE A8;>2>5 ?>;5 ?>B5=F80;L=> 8, A;54>20B5;L=>, ?>B5=F80;L=0O M=5@38O U =5 7028A8B >B 2@5<5=8: U = U ( x , y , z ) .
AB0F8>=0@=KE A>AB>O=8OE A>AB>O=85 G0AB8FK 2 40==K9 <><5=B 2@5<5=8 >?8AK205BAO ?5@8>48G5A:>9 DC=:F859 2@5<5=8 ! A F8:;8G5A:>9 G0AB>B>9 w ( ><M30) . @8 MB>< !- DC=:F8O >?@545;O5BAO ?>;=>9 M=5@3859 G0AB8FK.
!B0F8>=0@=>5 C@02=5=85 (@Q48=35@0: [ B@5C3>;L=8:] ?A8( <0;5=L:>5) + ( 2 * m / h ( A G5@B>9) ^ 2 ) * ( E - U ) * ?A8( <0;5=L:>5) = 0 .
20=B>20=85 M=5@388. #GB5<, GB> D878G5A:89 A<KA; 8<5NB ;8HL B0:85 @5H5=8O C@02=5=8O( BCB 8 40;55 3>2>@8BAO ?@> AB0F8>=0@=>5) , :>340 =52@5<5==0O 2>;=>20O DC=:F8O ?A8( <0;5=L:>5) ( [ 25:B>@] r ) 8 55 ?5@2K5 ?@>872>4=K5 ?> :>>@48=0B0< C4>2;5B2>@ONB AB0=40@B=K< CA;>28O<. -B8 CA;>28O O2;ONBAO B@51>20=8O<8, =0:;04K205<K<8 =0 8A:><>5 @5H5=85 48DD5@5=F80;L=>3> C@02=5=8O. 5H5=8O C@02=5=8O (@Q48=35@0, C4>2;5B2>@ONI85 MB8< CA;>28O<, >:07K20NBAO 2>7<>6=K<8 ;8HL ?@8 =5:>B>@KE 7=0G5=8OE M=5@388 , =07K205<KE A>1AB25==K<8 7=0G5=8O<8 M=5@388. $C=:F88 ?A8, O2;ONI85AO @5H5=8O<8 C@02=5=8O ?@8 MB8E 7=0G5=8OE M=5@388, =07K20NBAO A>1AB25==K<8 DC=:F8O<8, ?@8=04;560I8<8 A>1AB25==K< 7=0G5=8O< .
!>1AB25==K5 7=0G5=8O <>3CB >1@07>2K20BL :0: =5?@5@K2=K9, B0: 8 48A:@5B=K9 @O4. ?5@2>< A;CG05 3>2>@OB > =5?@5@K2=>< ( A?;>H=><) A?5:B@5 M=5@388, 2> 2B>@>< > 55 48A:@5B=>< A?5:B@5.
#@02=5=85 (@Q48=35@0 O2;O5BAO <0B5<0B8G5A:8< 2K@065=85< :>@?CA:C;O@=>- 2>;=>2>3> 4C0;87<0. => C4>2;5B2>@O5B ?@8=F8?C A>>B25BAB28O >@0 8 2 ?@545;L=>< A;CG05, :>340 4;8=0 2>;=K 45 @>9;O 7=0G8B5;L=> <5=LH5 @07<5@>2, E0@0:B5@=KE 4;O @0AA<0B@8205<>3> 42865=8O, ?>72>;O5B >?8A0BL 42865=85 G0AB8F ?> 70:>=0< :;0AA8G5A:>9 <5E0=8:8.
Соседние файлы в папке Кратко