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3
2.5
2
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
3
θ
1
0.8
0.6
0.4
0.2
0
0
0.5
1
1.5
2
2.5
3
φ
Figure 30.
Extremal trajectories for
= 4 . 5, γ + = 2, and γ =− 0 . 5. The equations of the
γ | 1 +
2 / (1 +
dashed lines are ϕ
=
π
arctan(1 / ) and ρ
=|
γ + ) (see the text). Numerical
values of the parameters are taken to be ϕ (0) =
π/ 4, p θ = 2, p ρ (0) = 0 . 1, and ρ (0) = 1. p ϕ (0) is
successively equal to -10, -2.5, 0, 2.5, and 10 for the different extremals.
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