1 
Biv) == | Fixy2(v- dx 
O 2m | {x /2@-0e| 
R 
1 
= ¥(v— U(x) dx 
i fa ann 
R 
A(v) |= 
2) v-U@) 
R 
The integration range R is such that U(x) < v. The general stationary solution is given as 
Pv) = lim p(vlvo; 1) = KAW) of (2 2o)} (12.88) 
where 
Vv 
_ {2© 
O(v) = | C® (12.89) 
0 
and k is a normalizing constant. Then, from the relation of v, x, y(= x) and reverting to 
the original x,y variables, 
1 
p(x, y) = Jim p(, ylxo, yo; t) = C oo (# Jo a + U(x) } (12.90) 
When the equation of motion is expressed as 
X + Wowox(1 + elx!") +6 x = n(t), (12.91) 
NOW Wo being the natural frequency of the linear (€ = 0) system, Eq. 12.90 becomes 
n+2 
1 
P(x, y) = C polx, y) exp4 — Gn€* ate +y’) 
where 
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