Осцилятор Дуффинга. Астахов В.В - 41 стр.

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B << 1, |ω
ω
0
| << 1
x(t) = Re [a(t) exp (
0
t)] ,
a(t)
x(t) =
1
2
[a exp (
0
t) + a
exp (
0
t)] ,
a
˙a exp (
0
t) + ˙a
exp (
0
t) = 0.
˙x(t) =
1
2
[˙a exp (
0
t) +
0
a exp (
0
t) + ˙a
exp (
0
t)
0
a
exp (
0
t)]
=
1
2
[
0
a exp (
0
t)
0
a
exp (
0
t)] .
¨x(t) =
1
2
0
˙a exp (
0
t) ω
2
0
a exp (
0
t)
0
˙a
exp (
0
t) ω
2
0
a
exp (
0
t)
=
0
˙a exp (
0
t)
ω
2
0
2
[a exp (
0
t) + a
exp (
0
t)] .