LumpedParameter Electromechanics
From this expression we can now evaluate the mechanical forces of electric origin
fl
and
f2
e
(mechanical terminal relations);
thus
8We
2
S
1
aS
as
2
fie(ql, q
2
,x1,
x2)
=

=
 q
1
2

q
1
q
2
S

1q
2
2
,
(e)
w,
2
as
asa
a
ass
f
2
e(q
1
, q
2
,
x1,
x
2
)
=
=
q
2
91q
2
a

q22
(f)
Because
S
1
,
S
2,
and
S,
are known
as
functions of
zx
and
x
2
for
this
example,
the
derivatives
in (e) and
(f)
can
be
calculated;
this is
straightforward differentiation, however, and is not
carried
out
here.
3.1.2b
ForceCoenergy Relations
So far in the magnetic field examples the flux linkage
A
has been used as the
independent variable, with current
i
described by the terminal relation.
Similarly, in electric field examples charge
q
has been used as the independent
variable, with voltage
v
described
by
the terminal relation. These choices
were natural because of the form of the conservation of energy equations
(3.1.9)
and
(3.1.13).
Note that in Example
3.1.1
we were required to find
vI(ql,
q
2
)
and
v,(ql,
q
2
).
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 Fall '11
 Liu
 Magnetic Field, terminal relation

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