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Arnold's Trivium
1991 Arnold's Trivium
27
Problem 27
Problem 27
Source:
July 1, 2010
Problem Statement
Sketch the images of the solutions of the equation
x
¨
=
F
(
x
)
−
k
x
˙
,
F
=
−
d
U
/
d
x
\ddot{x}=F(x)-k\dot{x},\; F=-dU/dx
x
¨
=
F
(
x
)
−
k
x
˙
,
F
=
−
d
U
/
d
x
in the
(
x
,
E
)
(x,E)
(
x
,
E
)
-plane, where
E
=
x
˙
2
/
2
+
U
(
x
)
E=\dot{x}^2/2+U(x)
E
=
x
˙
2
/2
+
U
(
x
)
, near non-degenerate critical points of the potential
U
U
U
.
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