STURM-LIOUVILLE DIFFERENCE EQUATIONS
(1.1.7) V(c„Ay„) =
anw2yn
, n = l , . . . , m - l .
1.2 Network Theory
1
Consider a cascade of LC circuits with inductance an, capacitance —, and
loop current un in the successive meshes (see Figure 1.2).
«-.
t,
J*
V^-d=r yCe-d=r v ^
V c
^ VcJ=
&
t
Figure 1.2: LONetwork
1 .
The current in the branch containing is un tin+i in the sense of un.
cn
Assume that un is of the form
ynctwtj
where yn is a complex constant, and, for
the nonhomogeneous problem, assume that a generator in the first mesh supplies
a voltage Eeiwt. Then, by KirchofTs rule, it follows that
(1.2.1) E + c-iyo(iw)~l + aoyoiw + c0(y0 - yi)(ttn)"1 = 0 ,
and, for n = 1,..., m 1,
(1.2.2) cn-x(yn - yn-i)(iw)~l + anyniw + cn(yn - yn+i)(iw)~l = 0.
Note that y_i = ym = 0, so that multiplication by iw in (1.2.1) and (1.2.2) gives
V(c0Ay0) =
aow2yo
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