Abstract
In this paper we shall do concerned with the simultaneous differential equations
dx
/
dt
=
μξ
dy
/
dt
=
λ
(
x
) +
μη
, (1) where
λ
(
x
) is a function of
x
only and
ξ
and
η
are functions of
x
and
y
, periodic in
y
with period 2
π
and expressible as Fourier series in sines and cosines of multiples of
y
, the coefficients being functions of
x
not involving
t
explicitly,
μ
is simply a constant parameter. These equations are a generalisation of the equation for the triode oscillator. Appleton and van der Pol have shown that, in the free triode, the anode potential
v
is determined by a differential equation of the type
d
2
v
/
dt
2
+
f
(
v
)
dv
/
dt
+
ω
2
v
= 0, (i) where
f
(
v
) is expressible as a power series in
v
of the type
f
(
v
) = -
α
+
βv
+
γv
2
+ ... , (ii) the coefficients
α, β, γ
, etc., being small compared with
ω
.
Cited by
6 articles.
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1. Frequency-amplitude characteristics of periodic motions in a periodically forced van der Pol oscillator;The European Physical Journal Special Topics;2019-09
2. Introduction;Oscillators and Oscillator Systems;1999
3. Periodic solutions of Liénard systems;Journal of Mathematical Analysis and Applications;1978-01
4. BIBLIOGRAPHY;Frequency of Self-Oscillations;1964
5. The Nonlinear Theory of Electric Oscillations;Proceedings of the IRE;1934-09