TeorijaEKola08 Laplace.pdf
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Transcript of TeorijaEKola08 Laplace.pdf
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. , , , , , 2015.
=
0
de)()( ttusU ts
+
pi=
j
jde)(
2j1)(
c
c
ts ssUtu
.
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. , , , , , 2015.
=
0
de)()( ttusU ts
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. , , , , , 2015.
, (), ()
()
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. , , , , , 2015.
-
()
, ,
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Initial value problems
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. , , , , , 2015.
:
( )
()
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. , , , , , 2015.
=
0
de)()( ttusU ts
)()()( ttwtu =
))((LT)())(LT()(
1 sUtu
tusU
=
=
w(t) ,
,
,
+
pi=
j
jde)(
2j1)(
c
c
ts ssUtu
c
)R,(,j +=s
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. , , , , , 2015.
,
u(t) (, /)
U(s) (, /, , )
LT(u(t)) LT-1(U(s))
s (. .) u(t) U(s)
.
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. , , , , , 2015.
c .
. , ,
.
.
-
-
u(t)
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. , , , , , 2015.
LT
)()()()( 2121 sUsUtutu ==
)()())()(LT( 2121 sUbsUatubtua +=+
)0()()d
)(dLT( = usUst
tu
))(LT()())(LT()(
))(LT()(
22
11tusU
tusUtusU
=
=
=
const, =ba
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. , , , , , 2015.
() LT ,
u(t), ctKtu e)( Re(s) > c (ROC, region of convergence).
:
0)(lim)Re(
=
sU
s U(s)
ksUss
s=
)(lim)(
0 u(t) ktu
tt
=
)(lim)0(
R0
>
c
K
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. , , , , , 2015.
t-, s-
t- u(t) ( )
s- U(s)( )
, s,
,
, LT, u(t) , . U(s)
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LT
(t).
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. , , , , , 2015.
LT (1)
(t).
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LT (2)
(t).
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. , , , , , 2015.
sUsU
Ts
=
e1)(g
TsTsUsU
Ts
2g)1(e1)( +=
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.
s
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. , , , , , 2015.
LT
,
,
(
) , ,
-
00 =t
0t
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. , , , , , 2015.
, , :
, -
( )
( ) ( )
-
. , , , , , 2015.
LT
L C
p1 p2
0I 0U00 =t021 =+ ii
021 = uu
t
iLudd 1
1 =
t
uCid
d 22 =
001 )( Iti =
002 )( Utu =
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. , , , , , 2015.
LT
021 =+ ii
021 = uu
t
iLudd 1
1 =
t
uCid
d 22 =
0)LT( 21 =+ ii0)LT( 21 = uu
)ddLT()LT( 11 tiLu =
)d
dLT()LT( 22 tuCi =
LT
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. , , , , , 2015.
LT
0)LT( 21 =+ ii0)LT( 21 = uu
)ddLT()LT( 11 tiLu =
)d
dLT()LT( 22 tuCi =
0)LT()LT( 21 =+ ii0)LT()LT( 21 = uu
)ddLT()LT( 11 tiLu =
)d
dLT()LT( 22 tuCi =
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. , , , , , 2015.
LT
0)()( 21 =+ sIsI0)()( 21 = sUsU
))(()( 011 IsIsLsU =
))(()( 022 UsUsCsI =
0)LT()LT( 21 =+ ii0)LT()LT( 21 = uu
)ddLT()LT( 11 tiLu =
)d
dLT()LT( 22 tuCi =
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. , , , , , 2015.
LT
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:
))((LT)( 111 sIti =
L C
p1 p2
0I 0U
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. , , , , , 2015.
)1
)((LT))((LT)( 2001
11
1+
+==
sCLUIsLC
sIti
)1
(LT)1
(LT)11
(LT)( 201
201
20
201
1+
++
=
++
+=
sCLCU
sCLIsCL
sCLCU
sCLIsCL
ti
)1
1
(LT)1
(LT)( 22
102
2
101
+
+
+
=
CLs
CLLCU
CLs
sIti
)1sin()1cos()( 001 tCLLCUt
CLIti += 0>t
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-
-
( )
, ,
( , , , )
( )
-
. , , , , , 2015.
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. , , , , , 2015.
)()()d)()(LT(0
sGsUtgut
=
TssUTtu = e)())(LT(
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. , , , , , 2015.
))((lim)0( sUsus
+=
))((lim)(0
sUsus
=
, ,
.
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. , , , , , 2015.
()
TssUTtu = e)())(LT(
attuasU =+ e)())((LT 1
, ,
.
-
. , , , , , 2015.
)()()d)()(LT(0
sGsUtgut
=
-
. , , , , , 2015.
()
)(1))(LT(a
sUa
atu =
)(1))((LT 1a
tu
asaU =
0R
>
a
a
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. , , , , , 2015.
t-
)0()())(LT( = usUstu
)0()0()())(LT( 2 = ususUstu
)0()0()0()0()())(LT(
)1()2(
21)(
=
nn
nnnn
usu
sususUstu L
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. , , , , , 2015.
s-
s
sUtut
d)(d)1())(LT( =
n
nnn
s
sUtut
d)(d)1())(LT( =
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. . .
( )
-
(. , )
, ( )
, (, )
. ( , s)
-
. , , , , , 2015.
, ,
, ,
() () ( , voltage gain,
voltage amplification) ( , current gain,
current amplification) (attenuation)
,
, .
-
. , , , , , 2015.
. . .
:
: ,
-
. , , , , , 2015.
))((LT)( 1 sHtg =
))(1(LT)( 1 sHs
tf =
( ) *
( ) * s
h(t)
Unit-impulse response
Unit-step response
*,
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LT
s .
-
. , , , , , 2015.
. ?
,
H = 1.
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m : 1
ug
C
L u
i
)()1sin()( mg ttCLUtu =
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. ?
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. , , , , , 2015.
. LT
,
( ) .
?
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. , , , , , 2015.
(1) ?
? ? ? ?
?
?
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(2) ?
? ? ?
?
( ) ?
() ?
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(3)
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(4)
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(5)
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(6)
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(1)
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(2)
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(3)
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(4)
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(5)
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(6)
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(7)
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(8)
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(9)
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(10)
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(11)
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Pierre-Simon Laplace 17491827
. Jean d'Alembert. Simon Denis Poisson. coleMilitaire. Acadmie des sciences. . Beaumont-en-Auge, .
1785
Je n'avais pas besoin de cette hypothse-l.
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Pierre Simon (Marquis de) Laplace 17491827http://www.tour-eiffel.fr/
