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Файл:шпоры для зачета у Хановой / 37.динам.издерж. В кратко
.txt яю 3 7 . 8=0<8:0 8745@65: 2 :@0B:>A@>G=>< ?5@8>45.
>AB>O==K5 8745@6:8 ( F C ) MB> @0AE>4K, :>B>@K5 >AB0NBAO =587<5==K<8 =57028A8<> >B :>;8G5AB20 ?@>872>48<>9 ?@>4C:F88. =8< >B=>AOB: 25;8G8=C 0@5=4=>9 ?;0BK, ?>2@5<5==0O 70@?;0B0, =0G8A;5=85 =0;>3>2, 0<>@B870F8>==>5 =0G8A;5=85.
5@5<5==K5 8745@6:8 ( V C ) <5=ONBAO 2 7028A8<>AB8 >B >1J5<0 ?@>872>4AB20. !2O70=K A 70B@0B0<8 =0 ?>:C?:C AK@LO, <0B5@80;>2, B>?;820, M=5@388 8 >?;0BC A45;L=>9 70@?;0BK.
8=0<8:0 ?5@5<5==KE 8745@65: =5@02=><5@=0. 0G8=0O A =C;O ?> <5@5 =0G0;0 ?@>872>4AB20, >=8 @0ABCB 1KAB@>, B. :. ?@8E>4OBAO =0 =57=0G8B5;L=K9 >1J5< ?@>872>4AB20. 0B5< ?> <5@5 40;L=59H53> C25;8G5=8O >1J5<0 ?@- 20 =0G8=05B A:07K20BLAO D0:B>@ M:>=><88. 0 <0AA>2>< ?@>87- 25 @>AB ?5@5<5==KE 8745@65: AB0=>28BAO 1>;55 <54;5==K<. 40;L=59H5< ?5@5<5==K5 8745@6:8 A=>20 =0G8=0NB AB@5<8B5;L=> @0AB8, >13>=OO @>AB ?@>87- 20, B. :. 2ABC?05B 2 459AB285 7- = C1K20NI59 ?@545;L=>9 ?@>872>48B5;L=>AB8.
1I85 20;>2K5 8745@6:8 ( T C ) ?@54AB02;ONB A>1>9 AC<<C ?>AB>O==KE 8 ?5@5<5==KE 8745@65: ?@8 :064>< :>=:@5B=>< C@>2=5 ?@>87- 20. T C = F C + V C
!@54=85 8745@6:8 ( "!) ?>:07K20NB 70B@0BK, ?@8E>4OI85AO =0 548=8FC ?@>4C:F88. "!= "!/ Q . !@54=85 8745@6:8 8<5NB 1>;LH>5 7=0G5=85 4;O ?@54?@8=8<0B5;O, B. :. ?>72>;ONB >?@545;8BL, ?@8 :0:>< >1J5<5 ?@>87- 20 8745@6:8 =0 548=8FC ?@>4C:B0 1C4CB <8=8<0;L=K. A F C = F C / Q , A V C = V C / Q , A T C = A F C = A V C >1I85 A@54=85
5@2>=0G0;L=> A@54=85 >1I85 8745@6:8 2KA>:8, B. :. =0 =8E 2;8O5B 25;8G8=0 ?>AB>O==KE 8745@65:, :>B>@0O @0A?@545;O5BAO =0 =57=0G8B5;L=K9 >1J5< ?@>4C:F88. > <5@5 @>AB0 ?@>87- 20 ?>AB>O==K5 8745@6:8 ?@8E>4OBAO =0 2A5 1>;LH55 G8A;> 548=8F ?@>4C:F88 8 A "! 1KAB@> ?0405B, 4>E>4O 4> <8=8<0;L=>3> A2>53> 7=0G5=8O. 0G5< =0G8=05B A:07K20BLAO D0:B>@ C25;8G5=8O ?5@5<5==KE 8745@65: 2 A;54AB285 7- =0 C1K20NI59 ?@545;L=>9 >B40G8.
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
>AB>O==K5 8745@6:8 ( F C ) MB> @0AE>4K, :>B>@K5 >AB0NBAO =587<5==K<8 =57028A8<> >B :>;8G5AB20 ?@>872>48<>9 ?@>4C:F88. =8< >B=>AOB: 25;8G8=C 0@5=4=>9 ?;0BK, ?>2@5<5==0O 70@?;0B0, =0G8A;5=85 =0;>3>2, 0<>@B870F8>==>5 =0G8A;5=85.
5@5<5==K5 8745@6:8 ( V C ) <5=ONBAO 2 7028A8<>AB8 >B >1J5<0 ?@>872>4AB20. !2O70=K A 70B@0B0<8 =0 ?>:C?:C AK@LO, <0B5@80;>2, B>?;820, M=5@388 8 >?;0BC A45;L=>9 70@?;0BK.
8=0<8:0 ?5@5<5==KE 8745@65: =5@02=><5@=0. 0G8=0O A =C;O ?> <5@5 =0G0;0 ?@>872>4AB20, >=8 @0ABCB 1KAB@>, B. :. ?@8E>4OBAO =0 =57=0G8B5;L=K9 >1J5< ?@>872>4AB20. 0B5< ?> <5@5 40;L=59H53> C25;8G5=8O >1J5<0 ?@- 20 =0G8=05B A:07K20BLAO D0:B>@ M:>=><88. 0 <0AA>2>< ?@>87- 25 @>AB ?5@5<5==KE 8745@65: AB0=>28BAO 1>;55 <54;5==K<. 40;L=59H5< ?5@5<5==K5 8745@6:8 A=>20 =0G8=0NB AB@5<8B5;L=> @0AB8, >13>=OO @>AB ?@>87- 20, B. :. 2ABC?05B 2 459AB285 7- = C1K20NI59 ?@545;L=>9 ?@>872>48B5;L=>AB8.
1I85 20;>2K5 8745@6:8 ( T C ) ?@54AB02;ONB A>1>9 AC<<C ?>AB>O==KE 8 ?5@5<5==KE 8745@65: ?@8 :064>< :>=:@5B=>< C@>2=5 ?@>87- 20. T C = F C + V C
!@54=85 8745@6:8 ( "!) ?>:07K20NB 70B@0BK, ?@8E>4OI85AO =0 548=8FC ?@>4C:F88. "!= "!/ Q . !@54=85 8745@6:8 8<5NB 1>;LH>5 7=0G5=85 4;O ?@54?@8=8<0B5;O, B. :. ?>72>;ONB >?@545;8BL, ?@8 :0:>< >1J5<5 ?@>87- 20 8745@6:8 =0 548=8FC ?@>4C:B0 1C4CB <8=8<0;L=K. A F C = F C / Q , A V C = V C / Q , A T C = A F C = A V C >1I85 A@54=85
5@2>=0G0;L=> A@54=85 >1I85 8745@6:8 2KA>:8, B. :. =0 =8E 2;8O5B 25;8G8=0 ?>AB>O==KE 8745@65:, :>B>@0O @0A?@545;O5BAO =0 =57=0G8B5;L=K9 >1J5< ?@>4C:F88. > <5@5 @>AB0 ?@>87- 20 ?>AB>O==K5 8745@6:8 ?@8E>4OBAO =0 2A5 1>;LH55 G8A;> 548=8F ?@>4C:F88 8 A "! 1KAB@> ?0405B, 4>E>4O 4> <8=8<0;L=>3> A2>53> 7=0G5=8O. 0G5< =0G8=05B A:07K20BLAO D0:B>@ C25;8G5=8O ?5@5<5==KE 8745@65: 2 A;54AB285 7- =0 C1K20NI59 ?@545;L=>9 >B40G8.
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