Quasi-Periodic Motion Around the
Collinear Equilibrium Points for the
Restricted Three Body Problem
Working Seminar in Celestial Mechanics
by Ariadna Farrés
1
Quasi Periodic Motion Around L1 (Poinc Section z = 0)
h = 0.2
h = 0.4
0.4
0.6
0.3
0.4
0.2
0.2
x2
x2
0.1
0
-0.1
0
-0.2
-0.2
-0.4
-0.3
-0.4
-0.4
-0.3
-0.2
-0.1
0
x1
0.1
0.2
0.3
-0.6
-0.6
0.4
-0.4
-0.2
0
x1
h = 0.6
0.4
0.6
h = 0.8
0.8
1
0.6
0.8
0.6
0.4
0.4
x2
0.2
x2
0.2
0
0.2
0
-0.2
-0.2
-0.4
-0.4
-0.6
-0.8
-0.8
-0.6
-0.8
-0.6
-0.4
-0.2
0
x1
0.2
0.4
0.6
0.8
-1
-0.8
-0.6
-0.4
-0.2
0
x1
0.2
0.4
0.6
0.8
1
2
Quasi Periodic Motion Around L1 (Poinc Section Y = 0)
h = 0.2
h = 0.4
0.4
0.6
0.3
0.4
0.2
0.2
x4
x4
0.1
0
-0.1
0
-0.2
-0.2
-0.4
-0.3
-0.4
-0.5
-0.4
-0.3
-0.2
-0.1
0
x3
0.1
0.2
0.3
0.4
-0.6
-0.8
0.5
-0.6
-0.4
-0.2
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0.4
0.6
0.8
0
-0.2
-0.2
-0.4
-0.4
-0.6
-0.6
-0.8
-0.8
0.2
h = 0.8
0.8
x4
x4
h = 0.6
0
x3
-0.8
-0.6
-0.4
-0.2
0
x3
0.2
0.4
0.6
0.8
-1
-0.8
-0.6
-0.4
-0.2
0
x3
0.2
0.4
0.6
0.8
1
3
Quasi Periodic Motion Around L2 (Poinc Section z = 0)
h = 0.2
h = 0.4
0.4
0.6
0.3
0.4
0.2
0.2
x2
x2
0.1
0
-0.1
0
-0.2
-0.2
-0.4
-0.3
-0.4
-0.4
-0.3
-0.2
-0.1
0
x1
0.1
0.2
0.3
-0.6
-0.6
0.4
-0.4
-0.2
0
x1
h = 0.6
0.2
0.4
0.6
h = 0.8
0.8
1
0.6
0.8
0.6
0.4
0.4
0.2
x2
x2
0.2
0
0
-0.2
-0.2
-0.4
-0.4
-0.6
-0.6
-0.8
-0.8
-0.8
-1
-0.6
-0.4
-0.2
0
x1
0.2
0.4
0.6
0.8
-1
-0.8
-0.6
-0.4
-0.2
0
x1
0.2
0.4
0.6
0.8
1
4
Quasi Periodic Motion Around L2 (Poinc Section Y = 0)
h = 0.2
h = 0.4
0.5
0.8
0.4
0.6
0.3
0.4
0.2
0.2
x4
x4
0.1
0
-0.1
0
-0.2
-0.2
-0.4
-0.3
-0.6
-0.4
-0.5
-0.5
-0.4
-0.3
-0.2
-0.1
0
x3
0.1
0.2
0.3
0.4
-0.8
-0.8
0.5
-0.6
-0.4
-0.2
h = 0.6
0
x3
0.2
0.4
0.6
0.8
h = 0.8
0.8
1
0.6
0.8
0.6
0.4
0.4
0.2
x4
x4
0.2
0
0
-0.2
-0.2
-0.4
-0.4
-0.6
-0.6
-0.8
-0.8
-0.8
-1
-0.6
-0.4
-0.2
0
x3
0.2
0.4
0.6
0.8
-1
-0.8
-0.6
-0.4
-0.2
0
x3
0.2
0.4
0.6
0.8
1
5