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1
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C
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h
a
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[
2
]
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Un
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d
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[
3
]
.
T
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th
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UP
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h
a
s
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ter
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.
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is
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co
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to
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[
4
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UP
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ca
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[
5
]
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I
t
is
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p
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ac
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m
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w
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an
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v
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f
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.
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ase
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I
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t
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u
r
e
3
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e
m
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o
f
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ies an
d
s
h
u
n
t V
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C
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2
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ntr
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nt
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Me
an
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h
ile
th
e
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s
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s
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s
h
u
n
t
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ies
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h
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an
s
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ies
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o
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tr
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l
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as
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ec
ess
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o
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th
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r
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ig
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r
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s
w
ell.
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s
ca
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b
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ee
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in
Fig
u
r
e
3
(
a)
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d
3
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b
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,
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h
y
s
ter
esis
cu
r
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co
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tr
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ap
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lied
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f
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tr
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h
e
dq
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ce
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r
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tain
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th
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o
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p
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[
1
1
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th
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in
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(
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an
d
(
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-
(
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,
r
esp
ec
tiv
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Fu
r
th
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m
o
r
e,
th
e
r
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b
etw
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n
A
C
p
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w
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d
DC
p
o
w
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in
(
7
)
ca
n
b
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m
o
d
if
ied
as f
o
llo
w
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
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8
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C
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o
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Des
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f U
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1597
1
3
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1
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dc
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q
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atio
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ip
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ted
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tan
ce
an
d
in
d
u
ctan
ce
o
f
b
o
th
s
h
u
n
t
an
d
s
er
ies
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.
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th
e
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u
tp
u
t
v
o
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o
f
co
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ter
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s
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s
r
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n
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d
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o
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v
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v
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w
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th
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v
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d
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tr
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b
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as (
2
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d
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2
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r
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th
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u
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ce
r
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v
e
p
o
w
er
.
4.
DYNA
M
I
CS SYS
T
E
M
ANALYS
I
S
I
t
is
w
ell
k
n
o
w
n
th
at
th
e
d
y
n
am
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o
f
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tio
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s
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tem
w
ith
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UP
QC
ca
n
b
e
d
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ed
b
y
n
o
n
lin
ea
r
d
if
f
er
en
tial
eq
u
atio
n
s
y
s
tem
.
Ho
w
ev
er
,
th
e
n
o
n
lin
ea
r
s
y
s
tem
ca
n
b
e
ap
p
r
o
x
im
ated
b
y
lin
ea
r
izatio
n
ar
o
u
n
d
ce
r
tain
o
p
er
atin
g
co
n
d
itio
n
s
.
T
h
e
lin
ea
r
izatio
n
m
o
d
els
ca
n
b
e
u
s
ed
to
an
aly
ze
th
e
d
y
n
am
ic
p
er
f
o
r
m
an
ce
o
f
th
e
d
is
tr
ib
u
tio
n
s
y
s
tem
w
ith
th
e
UP
QC
.
4
.
1
.
L
inea
riza
t
io
n
a
nd
t
ra
ns
f
er
f
un
ct
io
n
A
m
ath
em
atica
l
m
o
d
el
o
f
th
e
d
is
tr
ib
u
tio
n
s
y
s
tem
w
it
h
th
e
UP
QC
th
at
is
f
o
u
n
d
in
(
1
)
-
(
3
)
an
d
(
1
0
)
-
(
2
1
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