estudo da estabilidade do movimento rotacional de
TRANSCRIPT
S586e
Silva, William Reis Estudo da estabilidade do movimento rotacional de satélites artificiais com variáveis canônicas / William Reis Silva – Guaratinguetá : [s.n], 2012. 167 f : il. Bibliografia: f. 108 - 111 Dissertação (Mestrado) – Universidade Estadual Paulista, Faculdade de Engenharia de Guaratinguetá, 2012. Orientador: Profª. Drª. Maria Cecília Franca de Paula Santos Zanardi Coorientador: Prof. Dr. Jorge Kennety Silva Formiga
1. Satélites artificiais 2. Movimento rotacional I. Título
CDU 629.783 (043)
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Região 2
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Reg ião 3
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0.0 0.2 0.4 0.6 0.80.0
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Região 5
0.0 0.2 0.4 0.6 0.80.0
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Região 6
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1º derivada hamiltoniana para e=0.nb 7
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1
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1
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�
3 �1 � 3 H2
G2� 1 � L12
L22L3 1 � L32
L22Cos�l2
4 L22�
3 �1 � 3 H2
G2� L1 �1 � L32
L22� Cos�2 l2
8 L22�
3 �1 � H
G�2
L1 �1 � L3
L2�2
Cos�2 g � 2 h � 2 l � 2 l2 � 2 l3
32 L22�
3 �1 � H
G�2
L12 �1 � L3
L2� 1 � L32
L22Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 1 � L12
L22L23
�
3 �1 � H
G�2
1 � L12
L22�1 � L3
L2� 1 � L32
L22Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 L2�
3 �1 � H
G�2
L12 �1 � L3
L2� 1 � L32
L22Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 1 � L12
L22L23
�
1º derivada hamiltoniana para e=0.nb 9
3 �1 � H
G�2
1 � L12
L22�1 � L3
L2� 1 � L32
L22Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 L2�
3 �1 � H
G�2
L1 �1 � L3
L2�2
Cos�2 g � 2 h � 2 l � 2 l2 � 2 l3
32 L22�
3 �1 � H
G�2
L1 �1 � L3
L2�2
Cos�2 g � 2 h � 2 l � 2 l2 � 2 l3
32 L22�
3 �1 � H
G�2
L12 �1 � L3
L2� 1 � L32
L22Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 1 � L12
L22L23
�
3 �1 � H
G�2
1 � L12
L22�1 � L3
L2� 1 � L32
L22Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 L2�
3 �1 � H
G�2
L12 �1 � L3
L2� 1 � L32
L22Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 1 � L12
L22L23
�
3 �1 � H
G�2
1 � L12
L22�1 � L3
L2� 1 � L32
L22Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 L2�
3 �1 � H
G�2
L1 �1 � L3
L2�2
Cos�2 g � 2 h � 2 l � 2 l2 � 2 l3
32 L22�
3 �1 � H
G� L1 �1 � L3
L2� 1 � L32
L22Cos�2 g � h � 2 l � 2 l2 � l3 Sin��
8 L22�
3 �1 � H
G� L12 �1 � 2 L3
L2� �1 � L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
8 1 � L12
L22L23
�
10 1º derivada hamiltoniana para e=0.nb
3 �1 � H
G� 1 � L12
L22�1 � 2 L3
L2� �1 � L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
8 L2�
3 �1 � H
G� L12 �1 � L3
L2� �1 � 2 L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
8 1 � L12
L22L23
�
3 �1 � H
G� 1 � L12
L22�1 � L3
L2� �1 � 2 L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
8 L2�
3 �1 � H
G� L1 �1 � L3
L2� 1 � L32
L22Cos�2 g � h � 2 l � 2 l2 � l3 Sin��
8 L22�
3 �1 � H
G� L1 �1 � L3
L2� 1 � L32
L22Cos�2 g � h � 2 l � 2 l2 � l3 Sin��
8 L22�
3 �1 � H
G� L12 �1 � L3
L2� �1 � 2 L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
8 1 � L12
L22L23
�
3 �1 � H
G� 1 � L12
L22�1 � L3
L2� �1 � 2 L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
8 L2�
3 �1 � H
G� L12 �1 � 2 L3
L2� �1 � L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
8 1 � L12
L22L23
�
3 �1 � H
G� 1 � L12
L22�1 � 2 L3
L2� �1 � L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
8 L2�
3 �1 � H
G� L1 �1 � L3
L2� 1 � L32
L22Cos�2 g � h � 2 l � 2 l2 � l3 Sin��
8 L22�
1º derivada hamiltoniana para e=0.nb 11
9 L1 �1 � L32
L22� Cos�2 g � 2 l � 2 l2 Sin��2
16 L22�
9 L12 L3 1 � L32
L22Cos�2 g � 2 l � l2 Sin��2
8 1 � L12
L22L24
�
9 1 � L12
L22L3 1 � L32
L22Cos�2 g � 2 l � l2 Sin��2
8 L22�
9 L12 L3 1 � L32
L22Cos�2 g � 2 l � l2 Sin��2
8 1 � L12
L22L24
�
9 1 � L12
L22L3 1 � L32
L22Cos�2 g � 2 l � l2 Sin��2
8 L22�
9 L1 �1 � L32
L22� Cos�2 g � 2 l � 2 l2 Sin��2
16 L22�
3 L1 �1 � L3
L2�2
Cos�2 h � 2 l2 � 2 l3 Sin��2
16 L22�
3 L12 �1 � L3
L2� 1 � L32
L22Cos�2 h � l2 � 2 l3 Sin��2
8 1 � L12
L22L23
�
3 1 � L12
L22�1 � L3
L2� 1 � L32
L22Cos�2 h � l2 � 2 l3 Sin��2
8 L2�
3 L12 �1 � L3
L2� 1 � L32
L22Cos�2 h � l2 � 2 l3 Sin��2
8 1 � L12
L22L23
�
3 1 � L12
L22�1 � L3
L2� 1 � L32
L22Cos�2 h � l2 � 2 l3 Sin��2
8 L2�
12 1º derivada hamiltoniana para e=0.nb
3 L1 �1 � L3
L2�2
Cos�2 h � 2 l2 � 2 l3 Sin��2
16 L22�
1
L223 L1 �
3
161 �
H
G
2
1 �L32
L22Cos�2 g � 2 h � 2 l � 2 l3 �
3
161 �
H
G
2
1 �L32
L22
Cos�2 g � 2 h � 2 l � 2 l3 �3
81 �
H
G1 �
L32
L22Cos�2 g � h � 2 l � l3 Sin�� �
3
81 �
H
G1 �
L32
L22Cos�2 g � h � 2 l � l3 Sin�� �
3
81 �
3 L32
L22Cos�2 g � 2 l Sin��2 �
3 L1 �1 � L3
L2� 1 � L32
L22Cos�h � 2 l2 � l3 Sin�2 �
8 L22�
3 L12 �1 � L3
L2� �1 � 2 L3
L2� Cos�h � l2 � l3 Sin�2 �
8 1 � L12
L22L23
�
3 1 � L12
L22�1 � L3
L2� �1 � 2 L3
L2� Cos�h � l2 � l3 Sin�2 �
8 L2�
3 L12 �1 � 2 L3
L2� �1 � L3
L2� Cos�h � l2 � l3 Sin�2 �
8 1 � L12
L22L23
�
3 1 � L12
L22�1 � 2 L3
L2� �1 � L3
L2� Cos�h � l2 � l3 Sin�2 �
8 L2�
3 L1 �1 � L3
L2� 1 � L32
L22Cos�h � 2 l2 � l3 Sin�2 �
8 L22�
1
L223 L1 �
1
2�
3
81 �
H2
G2�
L32
L22�
3 H2 L32
G2 L22�
3
81 �
L32
L22Cos�2 h � 2 l3 Sin��2 �
3 L3 1 � L32
L22Cos�h � l3 Sin�2 �
4 L2
D�F, L2� �
1º derivada hamiltoniana para e=0.nb 13
1
2
1
A�
1
BL2 � �
1
A�
1
Bcos l1 L2 �
1
2 L6
��A � B � 2 CC� M6 Μ4 �
3 �1 � 3 H2
G2� L1 1 � L12
L22L33 Cos�l2
4 L25 1 � L32
L22
�
3 �1 � 3 H2
G2� L13 L3 1 � L32
L22Cos�l2
4 1 � L12
L22L25
�
3 �1 � 3 H2
G2� L1 1 � L12
L22L3 1 � L32
L22Cos�l2
2 L23�
3 �1 � 3 H2
G2� �1 � L12
L22� L32 Cos�2 l2
8 L23�
3 �1 � 3 H2
G2� L12 �1 � L32
L22� Cos�2 l2
8 L23�
3 �1 � H
G�2 �1 � L12
L22� L3 �1 � L3
L2� Cos�2 g � 2 h � 2 l � 2 l2 � 2 l3
32 L22�
3 �1 � H
G�2
L12 �1 � L3
L2�2
Cos�2 g � 2 h � 2 l � 2 l2 � 2 l3
32 L23�
3 �1 � H
G�2
L1 1 � L12
L22L32 �1 � L3
L2� Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 L24 1 � L32
L22
�
3 �1 � H
G�2
L1 1 � L12
L22L3 1 � L32
L22Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 L23�
3 �1 � H
G�2
L13 �1 � L3
L2� 1 � L32
L22Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 1 � L12
L22L24
�
3 �1 � H
G�2
L1 1 � L12
L22�1 � L3
L2� 1 � L32
L22Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 L22�
14 1º derivada hamiltoniana para e=0.nb
3 �1 � H
G�2
L1 1 � L12
L22L32 �1 � L3
L2� Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 L24 1 � L32
L22
�
3 �1 � H
G�2
L1 1 � L12
L22L3 1 � L32
L22Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 L23�
3 �1 � H
G�2
L13 �1 � L3
L2� 1 � L32
L22Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 1 � L12
L22L24
�
3 �1 � H
G�2
L1 1 � L12
L22�1 � L3
L2� 1 � L32
L22Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 L22�
3 �1 � H
G�2 �1 � L12
L22� L3 �1 � L3
L2� Cos�2 g � 2 h � 2 l � 2 l2 � 2 l3
32 L22�
3 �1 � H
G�2
L12 �1 � L3
L2�2
Cos�2 g � 2 h � 2 l � 2 l2 � 2 l3
32 L23�
3 �1 � H
G�2 �1 � L12
L22� L3 �1 � L3
L2� Cos�2 g � 2 h � 2 l � 2 l2 � 2 l3
32 L22�
3 �1 � H
G�2
L12 �1 � L3
L2�2
Cos�2 g � 2 h � 2 l � 2 l2 � 2 l3
32 L23�
3 �1 � H
G�2
L1 1 � L12
L22L32 �1 � L3
L2� Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 L24 1 � L32
L22
�
3 �1 � H
G�2
L1 1 � L12
L22L3 1 � L32
L22Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 L23�
1º derivada hamiltoniana para e=0.nb 15
3 �1 � H
G�2
L13 �1 � L3
L2� 1 � L32
L22Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 1 � L12
L22L24
�
3 �1 � H
G�2
L1 1 � L12
L22�1 � L3
L2� 1 � L32
L22Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 L22�
3 �1 � H
G�2
L1 1 � L12
L22L32 �1 � L3
L2� Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 L24 1 � L32
L22
�
3 �1 � H
G�2
L1 1 � L12
L22L3 1 � L32
L22Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 L23�
3 �1 � H
G�2
L13 �1 � L3
L2� 1 � L32
L22Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 1 � L12
L22L24
�
3 �1 � H
G�2
L1 1 � L12
L22�1 � L3
L2� 1 � L32
L22Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 L22�
3 �1 � H
G�2 �1 � L12
L22� L3 �1 � L3
L2� Cos�2 g � 2 h � 2 l � 2 l2 � 2 l3
32 L22�
3 �1 � H
G�2
L12 �1 � L3
L2�2
Cos�2 g � 2 h � 2 l � 2 l2 � 2 l3
32 L23�
3 �1 � H
G� �1 � L12
L22� L32 �1 � L3
L2� Cos�2 g � h � 2 l � 2 l2 � l3 Sin��
16 L23 1 � L32
L22
�
3 �1 � H
G� �1 � L12
L22� L3 1 � L32
L22Cos�2 g � h � 2 l � 2 l2 � l3 Sin��
16 L22�
16 1º derivada hamiltoniana para e=0.nb
3 �1 � H
G� L12 �1 � L3
L2� 1 � L32
L22Cos�2 g � h � 2 l � 2 l2 � l3 Sin��
8 L23�
3 �1 � H
G� L1 1 � L12
L22L3 �1 � 2 L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
8 L23�
3 �1 � H
G� L1 1 � L12
L22L3 �1 � L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
4 L23�
3 �1 � H
G� L13 �1 � 2 L3
L2� �1 � L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
8 1 � L12
L22L24
�
3 �1 � H
G� L1 1 � L12
L22�1 � 2 L3
L2� �1 � L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
8 L22�
3 �1 � H
G� L1 1 � L12
L22L3 �1 � L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
4 L23�
3 �1 � H
G� L1 1 � L12
L22L3 �1 � 2 L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
8 L23�
3 �1 � H
G� L13 �1 � L3
L2� �1 � 2 L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
8 1 � L12
L22L24
�
3 �1 � H
G� L1 1 � L12
L22�1 � L3
L2� �1 � 2 L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
8 L22�
3 �1 � H
G� �1 � L12
L22� L32 �1 � L3
L2� Cos�2 g � h � 2 l � 2 l2 � l3 Sin��
16 L23 1 � L32
L22
�
1º derivada hamiltoniana para e=0.nb 17
3 �1 � H
G� �1 � L12
L22� L3 1 � L32
L22Cos�2 g � h � 2 l � 2 l2 � l3 Sin��
16 L22�
3 �1 � H
G� L12 �1 � L3
L2� 1 � L32
L22Cos�2 g � h � 2 l � 2 l2 � l3 Sin��
8 L23�
3 �1 � H
G� �1 � L12
L22� L32 �1 � L3
L2� Cos�2 g � h � 2 l � 2 l2 � l3 Sin��
16 L23 1 � L32
L22
�
3 �1 � H
G� �1 � L12
L22� L3 1 � L32
L22Cos�2 g � h � 2 l � 2 l2 � l3 Sin��
16 L22�
3 �1 � H
G� L12 �1 � L3
L2� 1 � L32
L22Cos�2 g � h � 2 l � 2 l2 � l3 Sin��
8 L23�
3 �1 � H
G� L1 1 � L12
L22L3 �1 � L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
4 L23�
3 �1 � H
G� L1 1 � L12
L22L3 �1 � 2 L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
8 L23�
3 �1 � H
G� L13 �1 � L3
L2� �1 � 2 L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
8 1 � L12
L22L24
�
3 �1 � H
G� L1 1 � L12
L22�1 � L3
L2� �1 � 2 L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
8 L22�
3 �1 � H
G� L1 1 � L12
L22L3 �1 � 2 L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
8 L23�
18 1º derivada hamiltoniana para e=0.nb
3 �1 � H
G� L1 1 � L12
L22L3 �1 � L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
4 L23�
3 �1 � H
G� L13 �1 � 2 L3
L2� �1 � L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
8 1 � L12
L22L24
�
3 �1 � H
G� L1 1 � L12
L22�1 � 2 L3
L2� �1 � L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
8 L22�
3 �1 � H
G� �1 � L12
L22� L32 �1 � L3
L2� Cos�2 g � h � 2 l � 2 l2 � l3 Sin��
16 L23 1 � L32
L22
�
3 �1 � H
G� �1 � L12
L22� L3 1 � L32
L22Cos�2 g � h � 2 l � 2 l2 � l3 Sin��
16 L22�
3 �1 � H
G� L12 �1 � L3
L2� 1 � L32
L22Cos�2 g � h � 2 l � 2 l2 � l3 Sin��
8 L23�
9 �1 � L12
L22� L32 Cos�2 g � 2 l � 2 l2 Sin��2
16 L23�
9 L12 �1 � L32
L22� Cos�2 g � 2 l � 2 l2 Sin��2
16 L23�
9 L1 1 � L12
L22L33 Cos�2 g � 2 l � l2 Sin��2
8 L25 1 � L32
L22
�
9 L13 L3 1 � L32
L22Cos�2 g � 2 l � l2 Sin��2
8 1 � L12
L22L25
�
9 L1 1 � L12
L22L3 1 � L32
L22Cos�2 g � 2 l � l2 Sin��2
4 L23�
9 L1 1 � L12
L22L33 Cos�2 g � 2 l � l2 Sin��2
8 L25 1 � L32
L22
�
9 L13 L3 1 � L32
L22Cos�2 g � 2 l � l2 Sin��2
8 1 � L12
L22L25
�
1º derivada hamiltoniana para e=0.nb 19
9 L1 1 � L12
L22L3 1 � L32
L22Cos�2 g � 2 l � l2 Sin��2
4 L23�
9 �1 � L12
L22� L32 Cos�2 g � 2 l � 2 l2 Sin��2
16 L23�
9 L12 �1 � L32
L22� Cos�2 g � 2 l � 2 l2 Sin��2
16 L23�
3 �1 � L12
L22� L3 �1 � L3
L2� Cos�2 h � 2 l2 � 2 l3 Sin��2
16 L22�
3 L12 �1 � L3
L2�2
Cos�2 h � 2 l2 � 2 l3 Sin��2
16 L23�
3 L1 1 � L12
L22L32 �1 � L3
L2� Cos�2 h � l2 � 2 l3 Sin��2
8 L24 1 � L32
L22
�
3 L1 1 � L12
L22L3 1 � L32
L22Cos�2 h � l2 � 2 l3 Sin��2
8 L23�
3 L13 �1 � L3
L2� 1 � L32
L22Cos�2 h � l2 � 2 l3 Sin��2
8 1 � L12
L22L24
�
3 L1 1 � L12
L22�1 � L3
L2� 1 � L32
L22Cos�2 h � l2 � 2 l3 Sin��2
8 L22�
3 L1 1 � L12
L22L32 �1 � L3
L2� Cos�2 h � l2 � 2 l3 Sin��2
8 L24 1 � L32
L22
�
3 L1 1 � L12
L22L3 1 � L32
L22Cos�2 h � l2 � 2 l3 Sin��2
8 L23�
20 1º derivada hamiltoniana para e=0.nb
3 L13 �1 � L3
L2� 1 � L32
L22Cos�2 h � l2 � 2 l3 Sin��2
8 1 � L12
L22L24
�
3 L1 1 � L12
L22�1 � L3
L2� 1 � L32
L22Cos�2 h � l2 � 2 l3 Sin��2
8 L22�
3 �1 � L12
L22� L3 �1 � L3
L2� Cos�2 h � 2 l2 � 2 l3 Sin��2
16 L22�
3 L12 �1 � L3
L2�2
Cos�2 h � 2 l2 � 2 l3 Sin��2
16 L23�
�1
2�
3 L12
2 L22�
3 �1 � H
G�2
L32 Cos�2 g � 2 h � 2 l � 2 l3
8 L23�
3 �1 � H
G�2
L32 Cos�2 g � 2 h � 2 l � 2 l3
8 L23�
3 �1 � H
G� L32 Cos�2 g � h � 2 l � l3 Sin��
8 L23 1 � L32
L22
�
3 �1 � H
G� L32 Cos�2 g � h � 2 l � l3 Sin��
8 L23 1 � L32
L22
�9 L32 Cos�2 g � 2 l Sin��2
4 L23�
1
L233 L12 �
3
161 �
H
G
2
1 �L32
L22Cos�2 g � 2 h � 2 l � 2 l3 �
3
161 �
H
G
2
1 �L32
L22
Cos�2 g � 2 h � 2 l � 2 l3 �3
81 �
H
G1 �
L32
L22Cos�2 g � h � 2 l � l3 Sin�� �
3
81 �
H
G1 �
L32
L22Cos�2 g � h � 2 l � l3 Sin�� �
3
81 �
3 L32
L22Cos�2 g � 2 l Sin��2 �
1º derivada hamiltoniana para e=0.nb 21
3 �1 � L12
L22� L32 �1 � L3
L2� Cos�h � 2 l2 � l3 Sin�2 �
16 L23 1 � L32
L22
�
3 �1 � L12
L22� L3 1 � L32
L22Cos�h � 2 l2 � l3 Sin�2 �
16 L22�
3 L12 �1 � L3
L2� 1 � L32
L22Cos�h � 2 l2 � l3 Sin�2 �
8 L23�
3 L1 1 � L12
L22L3 �1 � L3
L2� Cos�h � l2 � l3 Sin�2 �
4 L23�
3 L1 1 � L12
L22L3 �1 � 2 L3
L2� Cos�h � l2 � l3 Sin�2 �
8 L23�
3 L13 �1 � L3
L2� �1 � 2 L3
L2� Cos�h � l2 � l3 Sin�2 �
8 1 � L12
L22L24
�
3 L1 1 � L12
L22�1 � L3
L2� �1 � 2 L3
L2� Cos�h � l2 � l3 Sin�2 �
8 L22�
3 L1 1 � L12
L22L3 �1 � 2 L3
L2� Cos�h � l2 � l3 Sin�2 �
8 L23�
3 L1 1 � L12
L22L3 �1 � L3
L2� Cos�h � l2 � l3 Sin�2 �
4 L23�
3 L13 �1 � 2 L3
L2� �1 � L3
L2� Cos�h � l2 � l3 Sin�2 �
8 1 � L12
L22L24
�
22 1º derivada hamiltoniana para e=0.nb
3 L1 1 � L12
L22�1 � 2 L3
L2� �1 � L3
L2� Cos�h � l2 � l3 Sin�2 �
8 L22�
3 �1 � L12
L22� L32 �1 � L3
L2� Cos�h � 2 l2 � l3 Sin�2 �
16 L23 1 � L32
L22
�
3 �1 � L12
L22� L3 1 � L32
L22Cos�h � 2 l2 � l3 Sin�2 �
16 L22�
3 L12 �1 � L3
L2� 1 � L32
L22Cos�h � 2 l2 � l3 Sin�2 �
8 L23� �
1
2�
3 L12
2 L22
3
8�
2 L32
L23�
6 H2 L32
G2 L23�
3 L32 Cos�2 h � 2 l3 Sin��2
4 L23�
3 L33 Cos�h � l3 Sin�2 �
4 L24 1 � L32
L22
�
3 L3 1 � L32
L22Cos�h � l3 Sin�2 �
4 L22�
1
L233 L12 �
1
2�
3
81 �
H2
G2�
L32
L22�
3 H2 L32
G2 L22�
3
81 �
L32
L22Cos�2 h � 2 l3 Sin��2 �
3 L3 1 � L32
L22Cos�h � l3 Sin�2 �
4 L2
D�F, L3� �
1
2 L6��A � B � 2 CC� M6 Μ4
3 �1 � 3 H2
G2� L1 1 � L12
L22L32 Cos�l2
4 L24 1 � L32
L22
�
3 �1 � 3 H2
G2� L1 1 � L12
L221 � L32
L22Cos�l2
4 L22�
1º derivada hamiltoniana para e=0.nb 23
3 �1 � 3 H2
G2� �1 � L12
L22� L3 Cos�2 l2
8 L22�
3 �1 � H
G�2 �1 � L12
L22� �1 � L3
L2� Cos�2 g � 2 h � 2 l � 2 l2 � 2 l3
32 L2�
3 �1 � H
G�2
L1 1 � L12
L22L3 �1 � L3
L2� Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 L23 1 � L32
L22
�
3 �1 � H
G�2
L1 1 � L12
L221 � L32
L22Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 L22�
3 �1 � H
G�2
L1 1 � L12
L22L3 �1 � L3
L2� Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 L23 1 � L32
L22
�
3 �1 � H
G�2
L1 1 � L12
L221 � L32
L22Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 L22�
3 �1 � H
G�2 �1 � L12
L22� �1 � L3
L2� Cos�2 g � 2 h � 2 l � 2 l2 � 2 l3
32 L2�
3 �1 � H
G�2 �1 � L12
L22� �1 � L3
L2� Cos�2 g � 2 h � 2 l � 2 l2 � 2 l3
32 L2�
3 �1 � H
G�2
L1 1 � L12
L22L3 �1 � L3
L2� Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 L23 1 � L32
L22
�
3 �1 � H
G�2
L1 1 � L12
L221 � L32
L22Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 L22�
3 �1 � H
G�2
L1 1 � L12
L22L3 �1 � L3
L2� Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 L23 1 � L32
L22
�
24 1º derivada hamiltoniana para e=0.nb
3 �1 � H
G�2
L1 1 � L12
L221 � L32
L22Cos�2 g � 2 h � 2 l � l2 � 2 l3
16 L22�
3 �1 � H
G�2 �1 � L12
L22� �1 � L3
L2� Cos�2 g � 2 h � 2 l � 2 l2 � 2 l3
32 L2�
3 �1 � H
G� �1 � L12
L22� L3 �1 � L3
L2� Cos�2 g � h � 2 l � 2 l2 � l3 Sin��
16 L22 1 � L32
L22
�
3 �1 � H
G� �1 � L12
L22� 1 � L32
L22Cos�2 g � h � 2 l � 2 l2 � l3 Sin��
16 L2�
3 �1 � H
G� L1 1 � L12
L22�1 � 2 L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
8 L22�
3 �1 � H
G� L1 1 � L12
L22�1 � L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
4 L22�
3 �1 � H
G� L1 1 � L12
L22�1 � L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
4 L22�
3 �1 � H
G� L1 1 � L12
L22�1 � 2 L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
8 L22�
3 �1 � H
G� �1 � L12
L22� L3 �1 � L3
L2� Cos�2 g � h � 2 l � 2 l2 � l3 Sin��
16 L22 1 � L32
L22
�
3 �1 � H
G� �1 � L12
L22� 1 � L32
L22Cos�2 g � h � 2 l � 2 l2 � l3 Sin��
16 L2�
1º derivada hamiltoniana para e=0.nb 25
3 �1 � H
G� �1 � L12
L22� L3 �1 � L3
L2� Cos�2 g � h � 2 l � 2 l2 � l3 Sin��
16 L22 1 � L32
L22
�
3 �1 � H
G� �1 � L12
L22� 1 � L32
L22Cos�2 g � h � 2 l � 2 l2 � l3 Sin��
16 L2�
3 �1 � H
G� L1 1 � L12
L22�1 � L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
4 L22�
3 �1 � H
G� L1 1 � L12
L22�1 � 2 L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
8 L22�
3 �1 � H
G� L1 1 � L12
L22�1 � 2 L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
8 L22�
3 �1 � H
G� L1 1 � L12
L22�1 � L3
L2� Cos�2 g � h � 2 l � l2 � l3 Sin��
4 L22�
3 �1 � H
G� �1 � L12
L22� L3 �1 � L3
L2� Cos�2 g � h � 2 l � 2 l2 � l3 Sin��
16 L22 1 � L32
L22
�
3 �1 � H
G� �1 � L12
L22� 1 � L32
L22Cos�2 g � h � 2 l � 2 l2 � l3 Sin��
16 L2�
9 �1 � L12
L22� L3 Cos�2 g � 2 l � 2 l2 Sin��2
16 L22�
9 L1 1 � L12
L22L32 Cos�2 g � 2 l � l2 Sin��2
8 L24 1 � L32
L22
�
9 L1 1 � L12
L221 � L32
L22Cos�2 g � 2 l � l2 Sin��2
8 L22�
26 1º derivada hamiltoniana para e=0.nb
9 L1 1 � L12
L22L32 Cos�2 g � 2 l � l2 Sin��2
8 L24 1 � L32
L22
�
9 L1 1 � L12
L221 � L32
L22Cos�2 g � 2 l � l2 Sin��2
8 L22�
9 �1 � L12
L22� L3 Cos�2 g � 2 l � 2 l2 Sin��2
16 L22�
3 �1 � L12
L22� �1 � L3
L2� Cos�2 h � 2 l2 � 2 l3 Sin��2
16 L2�
3 L1 1 � L12
L22L3 �1 � L3
L2� Cos�2 h � l2 � 2 l3 Sin��2
8 L23 1 � L32
L22
�
3 L1 1 � L12
L221 � L32
L22Cos�2 h � l2 � 2 l3 Sin��2
8 L22�
3 L1 1 � L12
L22L3 �1 � L3
L2� Cos�2 h � l2 � 2 l3 Sin��2
8 L23 1 � L32
L22
�
3 L1 1 � L12
L221 � L32
L22Cos�2 h � l2 � 2 l3 Sin��2
8 L22�
3 �1 � L12
L22� �1 � L3
L2� Cos�2 h � 2 l2 � 2 l3 Sin��2
16 L2�
�1
2�
3 L12
2 L22
3 �1 � H
G�2
L3 Cos�2 g � 2 h � 2 l � 2 l3
8 L22�
3 �1 � H
G�2
L3 Cos�2 g � 2 h � 2 l � 2 l3
8 L22�
1º derivada hamiltoniana para e=0.nb 27
3 �1 � H
G� L3 Cos�2 g � h � 2 l � l3 Sin��
8 L22 1 � L32
L22
�3 �1 � H
G� L3 Cos�2 g � h � 2 l � l3 Sin��
8 L22 1 � L32
L22
�
9 L3 Cos�2 g � 2 l Sin��2
4 L22�
3 �1 � L12
L22� L3 �1 � L3
L2� Cos�h � 2 l2 � l3 Sin�2 �
16 L22 1 � L32
L22
�
3 �1 � L12
L22� 1 � L32
L22Cos�h � 2 l2 � l3 Sin�2 �
16 L2�
3 L1 1 � L12
L22�1 � L3
L2� Cos�h � l2 � l3 Sin�2 �
4 L22�
3 L1 1 � L12
L22�1 � 2 L3
L2� Cos�h � l2 � l3 Sin�2 �
8 L22�
3 L1 1 � L12
L22�1 � 2 L3
L2� Cos�h � l2 � l3 Sin�2 �
8 L22�
3 L1 1 � L12
L22�1 � L3
L2� Cos�h � l2 � l3 Sin�2 �
4 L22�
3 �1 � L12
L22� L3 �1 � L3
L2� Cos�h � 2 l2 � l3 Sin�2 �
16 L22 1 � L32
L22
�
3 �1 � L12
L22� 1 � L32
L22Cos�h � 2 l2 � l3 Sin�2 �
16 L2� �
1
2�
3 L12
2 L22
3
8
2 L3
L22�
6 H2 L3
G2 L22�
3 L3 Cos�2 h � 2 l3 Sin��2
4 L22�
3 L32 Cos�h � l3 Sin�2 �
4 L23 1 � L32
L22
�
3 1 � L32
L22Cos�h � l3 Sin�2 �
4 L2
28 1º derivada hamiltoniana para e=0.nb
a�A, CC, �� �
�1.54258� 10�6 � 2.06795� 10�25 A � 0.0000303794 A2 � 2.06795� 10�24 A3 � 2.3169� 10�10 A4 �
4.1359� 10�25 CC �1.54258� 10�6 CC
A� 0.0000607589 A CC � 1.98523� 10�23 A2 CC �
9.26759� 10�10 A3 CC � 0.0000303794CC2 �2.06795� 10�25 CC2
A� 1.98523� 10�23 A CC2 �
1.39014� 10�9 A2 CC2 � 2.06795� 10�24 CC3 �1.13772� 10�11 CC3
A� 9.26759� 10�10 A CC3 �
2.3169� 10�10 CC4 � 7.96522� 10�7 Sin�� � 0.000051155 A2 Sin�� � 2.64698� 10�23 A3 Sin�� �
8.69303� 10�11 A4 Sin�� �7.96522� 10�7 CC Sin��
A� 0.00010231 A CC Sin�� �
1.05879� 10�22 A2 CC Sin�� � 3.47721� 10�10 A3 CC Sin�� � 0.000051155 CC2 Sin�� �1.05879� 10�22 A CC2 Sin�� � 5.21582� 10�10 A2 CC2 Sin�� � 2.64698� 10�23 CC3 Sin�� �1.64096� 10�12 CC3 Sin��
A� 3.47721� 10�10 A CC3 Sin�� � 8.69303� 10�11 CC4 Sin�� �
9.36209� 10�7 Cos�� Sin�� � 8.27181� 10�25 A Cos�� Sin�� � 0.0000229674 A2 Cos�� Sin�� �2.64698� 10�23 A3 Cos�� Sin�� � 1.1117� 10�9 A4 Cos�� Sin�� � 1.65436� 10�24 CC Cos�� Sin�� �9.36209� 10�7 CC Cos�� Sin��
A� 0.0000459348 A CC Cos�� Sin�� �
5.29396� 10�23 A2 CC Cos�� Sin�� � 4.44678� 10�9 A3 CC Cos�� Sin�� �
0.0000229675CC2 Cos�� Sin�� �8.27181� 10�25 CC2 Cos�� Sin��
A�
5.29396� 10�23 A CC2 Cos�� Sin�� � 6.67017� 10�9 A2 CC2 Cos�� Sin�� �
2.64698� 10�23 CC3 Cos�� Sin�� �4.00342� 10�11 CC3 Cos�� Sin��
A�
4.44678� 10�9 A CC3 Cos�� Sin�� � 1.1117� 10�9 CC4 Cos�� Sin�� � 1.69596� 10�6 Sin��2 �
1.65436� 10�24 A Sin��2 � 0.0000876681 A2 Sin��2 � 6.08568� 10�10 A4 Sin��2 �
3.30872� 10�24 CC Sin��2 �1.69596� 10�6 CC Sin��2
A� 0.000175336 A CC Sin��2 �
2.11758� 10�22 A2 CC Sin��2 � 2.43427� 10�9 A3 CC Sin��2 � 0.0000876681CC2 Sin��2 �
1.65436� 10�24 CC2 Sin��2
A� 2.11758� 10�22 A CC2 Sin��2 � 3.65141� 10�9 A2 CC2 Sin��2 �
1.61439� 10�11 CC3 Sin��2
A� 2.43427� 10�9 A CC3 Sin��2 � 6.08568� 10�10 CC4 Sin��2 �
5.77228� 10�6 A2 Cos�� Sin��2 � 2.64698� 10�23 A3 Cos�� Sin��2 �
8.37815� 10�10 A4 Cos�� Sin��2 � 0.0000115446 A CC Cos�� Sin��2 �
1.05879� 10�22 A2 CC Cos�� Sin��2 � 3.35126� 10�9 A3 CC Cos�� Sin��2 �
5.7723� 10�6 CC2 Cos�� Sin��2 � 1.05879� 10�22 A CC2 Cos�� Sin��2 �
5.02689� 10�9 A2 CC2 Cos�� Sin��2 � 2.64698� 10�23 CC3 Cos�� Sin��2 �
1.03137� 10�11 CC3 Cos�� Sin��2
A� 3.35126� 10�9 A CC3 Cos�� Sin��2 �
8.37815� 10�10 CC4 Cos�� Sin��2 � 0.000042071 A2 Cos��2 Sin��2 �
1.32349� 10�23 A3 Cos��2 Sin��2 � 1.20417� 10�9 A4 Cos��2 Sin��2 �
0.000084142 A CC Cos��2 Sin��2 � 2.64698� 10�23 A2 CC Cos��2 Sin��2 �
4.8167� 10�9 A3 CC Cos��2 Sin��2 � 0.000042071 CC2 Cos��2 Sin��2 �
2.64698� 10�23 A CC2 Cos��2 Sin��2 � 7.22505� 10�9 A2 CC2 Cos��2 Sin��2 �
1.32349� 10�23 CC3 Cos��2 Sin��2 �1.75478� 10�11 CC3 Cos��2 Sin��2
A�
4.8167� 10�9 A CC3 Cos��2 Sin��2 � 1.20417� 10�9 CC4 Cos��2 Sin��2 �
0.0000357495 A2 Sin��3 � 5.29396� 10�23 A3 Sin��3 � 2.89353� 10�10 A4 Sin��3 �
0.000071499 A CC Sin��3 � 2.11758� 10�22 A2 CC Sin��3 � 1.15741� 10�9 A3 CC Sin��3 �
0.0000357495CC2 Sin��3 � 2.11758� 10�22 A CC2 Sin��3 � 1.73612� 10�9 A2 CC2 Sin��3 �
5.29396� 10�23 CC3 Sin��3 �1.09117� 10�12 CC3 Sin��3
A� 1.15741� 10�9 A CC3 Sin��3 �
2.89353� 10�10 CC4 Sin��3 � 0.0000144869 A2 Cos�� Sin��3 � 2.64698� 10�23 A3 Cos�� Sin��3 �
2.57923� 10�9 A4 Cos�� Sin��3 � 0.0000289737 A CC Cos�� Sin��3 �
1.03169� 10�8 A3 CC Cos�� Sin��3 � 0.0000144868CC2 Cos�� Sin��3 �
3.17637� 10�22 A CC2 Cos�� Sin��3 � 1.54754� 10�8 A2 CC2 Cos�� Sin��3 �
7.94093� 10�23 CC3 Cos�� Sin��3 �4.92704� 10�11 CC3 Cos�� Sin��3
A�
1.03169� 10�8 A CC3 Cos�� Sin��3 � 2.57923� 10�9 CC4 Cos�� Sin��3 �
3.59468� 10�11 A2 Cos��2 Sin��3 � 1.49367� 10�9 A4 Cos��2 Sin��3 �
1.07841� 10�10 A CC Cos��2 Sin��3 � 5.29396� 10�23 A2 CC Cos��2 Sin��3 �
5.97468� 10�9 A3 CC Cos��2 Sin��3 � 1.07841� 10�10 CC2 Cos��2 Sin��3 �
5.29396� 10�23 A CC2 Cos��2 Sin��3 � 8.96202� 10�9 A2 CC2 Cos��2 Sin��3 �
3.59468� 10�11 CC3 Cos��2 Sin��3
A� 5.97468� 10�9 A CC3 Cos��2 Sin��3 �
1.49367� 10�9 CC4 Cos��2 Sin��3 � 3.2381� 10�11 A2 Cos��3 Sin��3 �
1.32349� 10�23 A3 Cos��3 Sin��3 � 4.63875� 10�10 A4 Cos��3 Sin��3 �
9.7143� 10�11 A CC Cos��3 Sin��3 � 1.8555� 10�9 A3 CC Cos��3 Sin��3 �
9.7143� 10�11 CC2 Cos��3 Sin��3 � 2.78325� 10�9 A2 CC2 Cos��3 Sin��3 �
1.32349� 10�23 CC3 Cos��3 Sin��3 �3.2381� 10�11 CC3 Cos��3 Sin��3
A�
1.8555� 10�9 A CC3 Cos��3 Sin��3 � 4.63875� 10�10 CC4 Cos��3 Sin��3 �
1.03398� 10�25 A Sin��4 � 0.0000432135 A2 Sin��4 � 2.64698� 10�23 A3 Sin��4 �
7.49012� 10�10 A4 Sin��4 � 2.06795� 10�25 CC Sin��4 � 0.000086427 A CC Sin��4 �
1.58819� 10�22 A2 CC Sin��4 � 2.99605� 10�9 A3 CC Sin��4 � 0.0000432135CC2 Sin��4 �
1.03398� 10�25 CC2 Sin��4
A� 1.58819� 10�22 A CC2 Sin��4 � 4.49407� 10�9 A2 CC2 Sin��4 �
2 Função a e b para o satélite MP 2.nb
2.64698� 10�23 CC3 Sin��4 �7.92145� 10�12 CC3 Sin��4
A� 2.99605� 10�9 A CC3 Sin��4 �
7.49012� 10�10 CC4 Sin��4 � 4.33721� 10�12 A2 Cos�� Sin��4 � 5.29396� 10�23 A3 Cos�� Sin��4 �
1.43611� 10�9 A4 Cos�� Sin��4 � 1.30116� 10�11 A CC Cos�� Sin��4 �
1.05879� 10�22 A2 CC Cos�� Sin��4 � 5.74443� 10�9 A3 CC Cos�� Sin��4 �
1.30116� 10�11 CC2 Cos�� Sin��4 � 8.61665� 10�9 A2 CC2 Cos�� Sin��4 �
5.29396� 10�23 CC3 Cos�� Sin��4 �4.33721� 10�12 CC3 Cos�� Sin��4
A�
5.74443� 10�9 A CC3 Cos�� Sin��4 � 1.43611� 10�9 CC4 Cos�� Sin��4 �
2.14118� 10�11 A2 Cos��2 Sin��4 � 1.32349� 10�23 A3 Cos��2 Sin��4 �
2.40248� 10�9 A4 Cos��2 Sin��4 � 6.42355� 10�11 A CC Cos��2 Sin��4 �
2.64698� 10�23 A2 CC Cos��2 Sin��4 � 9.60991� 10�9 A3 CC Cos��2 Sin��4 �
6.42355� 10�11 CC2 Cos��2 Sin��4 � 2.64698� 10�23 A CC2 Cos��2 Sin��4 �
1.44149� 10�8 A2 CC2 Cos��2 Sin��4 � 1.32349� 10�23 CC3 Cos��2 Sin��4 �
2.14118� 10�11 CC3 Cos��2 Sin��4
A� 9.60991� 10�9 A CC3 Cos��2 Sin��4 �
2.40248� 10�9 CC4 Cos��2 Sin��4 � 1.61843� 10�12 A4 Cos��3 Sin��4 �
6.47374� 10�12 A3 CC Cos��3 Sin��4 � 9.71061� 10�12 A2 CC2 Cos��3 Sin��4 �
6.47374� 10�12 A CC3 Cos��3 Sin��4 � 1.61843� 10�12 CC4 Cos��3 Sin��4 �
4.68168� 10�10 A4 Cos��4 Sin��4 � 1.87267� 10�9 A3 CC Cos��4 Sin��4 �
2.80901� 10�9 A2 CC2 Cos��4 Sin��4 � 1.87267� 10�9 A CC3 Cos��4 Sin��4 �
4.68168� 10�10 CC4 Cos��4 Sin��4 � 4.23704� 10�12 A2 Sin��5 � 3.77078� 10�10 A4 Sin��5 �
1.27111� 10�11 A CC Sin��5 � 1.05879� 10�22 A2 CC Sin��5 � 1.50831� 10�9 A3 CC Sin��5 �
1.27111� 10�11 CC2 Sin��5 � 1.05879� 10�22 A CC2 Sin��5 � 2.26247� 10�9 A2 CC2 Sin��5 �
4.23704� 10�12 CC3 Sin��5
A� 1.50831� 10�9 A CC3 Sin��5 � 3.77078� 10�10 CC4 Sin��5 �
1.65874� 10�11 A2 Cos�� Sin��5 � 1.32349� 10�23 A3 Cos�� Sin��5 �
2.22631� 10�9 A4 Cos�� Sin��5 � 4.97623� 10�11 A CC Cos�� Sin��5 �
7.94093� 10�23 A2 CC Cos�� Sin��5 � 8.90526� 10�9 A3 CC Cos�� Sin��5 �
4.97623� 10�11 CC2 Cos�� Sin��5 � 7.94093� 10�23 A CC2 Cos�� Sin��5 �
1.33579� 10�8 A2 CC2 Cos�� Sin��5 � 1.32349� 10�23 CC3 Cos�� Sin��5 �
1.65874� 10�11 CC3 Cos�� Sin��5
A� 8.90526� 10�9 A CC3 Cos�� Sin��5 �
2.22631� 10�9 CC4 Cos�� Sin��5 � 1.45452� 10�9 A4 Cos��2 Sin��5 �
5.81809� 10�9 A3 CC Cos��2 Sin��5 � 8.72713� 10�9 A2 CC2 Cos��2 Sin��5 �
5.81809� 10�9 A CC3 Cos��2 Sin��5 � 1.45452� 10�9 CC4 Cos��2 Sin��5 �
5.97336� 10�10 A4 Cos��3 Sin��5 � 2.38934� 10�9 A3 CC Cos��3 Sin��5 �
3.58402� 10�9 A2 CC2 Cos��3 Sin��5 � 2.38934� 10�9 A CC3 Cos��3 Sin��5 �
5.97336� 10�10 CC4 Cos��3 Sin��5 � 7.55209� 10�13 A2 Sin��6 � 5.01478� 10�24 A3 Sin��6 �
3.86272� 10�10 A4 Sin��6 � 2.26563� 10�12 A CC Sin��6 � 2.63664� 10�24 A2 CC Sin��6 �
1.54509� 10�9 A3 CC Sin��6 � 2.26563� 10�12 CC2 Sin��6 � 2.63664� 10�24 A CC2 Sin��6 �
Função a e b para o satélite MP 2.nb 3
2.31763� 10�9 A2 CC2 Sin��6 � 5.01478� 10�24 CC3 Sin��6 �7.55209� 10�13 CC3 Sin��6
A�
1.54509� 10�9 A CC3 Sin��6 � 3.86272� 10�10 CC4 Sin��6 � 6.78031� 10�10 A4 Cos�� Sin��6 �
2.71212� 10�9 A3 CC Cos�� Sin��6 � 4.06818� 10�9 A2 CC2 Cos�� Sin��6 �
2.71212� 10�9 A CC3 Cos�� Sin��6 � 6.78031� 10�10 CC4 Cos�� Sin��6 �
8.2031� 10�10 A4 Cos��2 Sin��6 � 3.28124� 10�9 A3 CC Cos��2 Sin��6 �
4.92186� 10�9 A2 CC2 Cos��2 Sin��6 � 3.28124� 10�9 A CC3 Cos��2 Sin��6 �
8.2031� 10�10 CC4 Cos��2 Sin��6 � 1.33511� 10�10 A4 Sin��7 � 5.34042� 10�10 A3 CC Sin��7 �
8.01063� 10�10 A2 CC2 Sin��7 � 5.34042� 10�10 A CC3 Sin��7 � 1.33511� 10�10 CC4 Sin��7 �
5.9621� 10�10 A4 Cos�� Sin��7 � 2.38484� 10�9 A3 CC Cos�� Sin��7 �
3.57726� 10�9 A2 CC2 Cos�� Sin��7 � 2.38484� 10�9 A CC3 Cos�� Sin��7 �
5.9621� 10�10 CC4 Cos�� Sin��7 � 1.66397� 10�11 A4 Sin��8 � 6.65588� 10�11 A3 CC Sin��8 �
9.98382� 10�11 A2 CC2 Sin��8 � 6.65588� 10�11 A CC3 Sin��8 � 1.66397� 10�11 CC4 Sin��8
b�A, CC, �� �
�1.54258� 10�6 � 2.06795� 10�25 A � 0.0000303794 A2 � 2.06795� 10�24 A3 � 2.3169� 10�10 A4 �
4.1359� 10�25 CC �1.54258� 10�6 CC
A� 0.0000607589 A CC � 1.98523� 10�23 A2 CC �
9.26759� 10�10 A3 CC � 0.0000303794CC2 �2.06795� 10�25 CC2
A� 1.98523� 10�23 A CC2 �
1.39014� 10�9 A2 CC2 � 2.06795� 10�24 CC3 �1.13772� 10�11 CC3
A� 9.26759� 10�10 A CC3 �
2.3169� 10�10 CC4 � 7.96522� 10�7 Sin�� � 0.000051155 A2 Sin�� � 2.64698� 10�23 A3 Sin�� �
8.69303� 10�11 A4 Sin�� �7.96522� 10�7 CC Sin��
A� 0.00010231 A CC Sin�� �
1.05879� 10�22 A2 CC Sin�� � 3.47721� 10�10 A3 CC Sin�� � 0.000051155 CC2 Sin�� �1.05879� 10�22 A CC2 Sin�� � 5.21582� 10�10 A2 CC2 Sin�� � 2.64698� 10�23 CC3 Sin�� �1.64096� 10�12 CC3 Sin��
A� 3.47721� 10�10 A CC3 Sin�� � 8.69303� 10�11 CC4 Sin�� �
9.36209� 10�7 Cos�� Sin�� � 8.27181� 10�25 A Cos�� Sin�� � 0.0000229674 A2 Cos�� Sin�� �2.64698� 10�23 A3 Cos�� Sin�� � 1.1117� 10�9 A4 Cos�� Sin�� � 1.65436� 10�24 CC Cos�� Sin�� �9.36209� 10�7 CC Cos�� Sin��
A� 0.0000459348 A CC Cos�� Sin�� �
5.29396� 10�23 A2 CC Cos�� Sin�� � 4.44678� 10�9 A3 CC Cos�� Sin�� �
0.0000229675CC2 Cos�� Sin�� �8.27181� 10�25 CC2 Cos�� Sin��
A�
4 Função a e b para o satélite MP 2.nb
5.29396� 10�23 A CC2 Cos�� Sin�� � 6.67017� 10�9 A2 CC2 Cos�� Sin�� �
2.64698� 10�23 CC3 Cos�� Sin�� �4.00342� 10�11 CC3 Cos�� Sin��
A�
4.44678� 10�9 A CC3 Cos�� Sin�� � 1.1117� 10�9 CC4 Cos�� Sin�� � 1.69596� 10�6 Sin��2 �
1.65436� 10�24 A Sin��2 � 0.0000876681 A2 Sin��2 � 6.08568� 10�10 A4 Sin��2 �
3.30872� 10�24 CC Sin��2 �1.69596� 10�6 CC Sin��2
A� 0.000175336 A CC Sin��2 �
2.11758� 10�22 A2 CC Sin��2 � 2.43427� 10�9 A3 CC Sin��2 � 0.0000876681CC2 Sin��2 �
1.65436� 10�24 CC2 Sin��2
A� 2.11758� 10�22 A CC2 Sin��2 � 3.65141� 10�9 A2 CC2 Sin��2 �
1.61439� 10�11 CC3 Sin��2
A� 2.43427� 10�9 A CC3 Sin��2 � 6.08568� 10�10 CC4 Sin��2 �
5.77228� 10�6 A2 Cos�� Sin��2 � 2.64698� 10�23 A3 Cos�� Sin��2 �
8.37815� 10�10 A4 Cos�� Sin��2 � 0.0000115446 A CC Cos�� Sin��2 �
1.05879� 10�22 A2 CC Cos�� Sin��2 � 3.35126� 10�9 A3 CC Cos�� Sin��2 �
5.7723� 10�6 CC2 Cos�� Sin��2 � 1.05879� 10�22 A CC2 Cos�� Sin��2 �
5.02689� 10�9 A2 CC2 Cos�� Sin��2 � 2.64698� 10�23 CC3 Cos�� Sin��2 �
1.03137� 10�11 CC3 Cos�� Sin��2
A� 3.35126� 10�9 A CC3 Cos�� Sin��2 �
8.37815� 10�10 CC4 Cos�� Sin��2 � 0.000042071 A2 Cos��2 Sin��2 �
1.32349� 10�23 A3 Cos��2 Sin��2 � 1.20417� 10�9 A4 Cos��2 Sin��2 �
0.000084142 A CC Cos��2 Sin��2 � 2.64698� 10�23 A2 CC Cos��2 Sin��2 �
4.8167� 10�9 A3 CC Cos��2 Sin��2 � 0.000042071 CC2 Cos��2 Sin��2 �
2.64698� 10�23 A CC2 Cos��2 Sin��2 � 7.22505� 10�9 A2 CC2 Cos��2 Sin��2 �
1.32349� 10�23 CC3 Cos��2 Sin��2 �1.75478� 10�11 CC3 Cos��2 Sin��2
A�
4.8167� 10�9 A CC3 Cos��2 Sin��2 � 1.20417� 10�9 CC4 Cos��2 Sin��2 �
0.0000357495 A2 Sin��3 � 5.29396� 10�23 A3 Sin��3 � 2.89353� 10�10 A4 Sin��3 �
0.000071499 A CC Sin��3 � 2.11758� 10�22 A2 CC Sin��3 � 1.15741� 10�9 A3 CC Sin��3 �
0.0000357495CC2 Sin��3 � 2.11758� 10�22 A CC2 Sin��3 � 1.73612� 10�9 A2 CC2 Sin��3 �
5.29396� 10�23 CC3 Sin��3 �1.09117� 10�12 CC3 Sin��3
A� 1.15741� 10�9 A CC3 Sin��3 �
2.89353� 10�10 CC4 Sin��3 � 0.0000144869 A2 Cos�� Sin��3 � 2.64698� 10�23 A3 Cos�� Sin��3 �
2.57923� 10�9 A4 Cos�� Sin��3 � 0.0000289737 A CC Cos�� Sin��3 �
1.03169� 10�8 A3 CC Cos�� Sin��3 � 0.0000144868CC2 Cos�� Sin��3 �
3.17637� 10�22 A CC2 Cos�� Sin��3 � 1.54754� 10�8 A2 CC2 Cos�� Sin��3 �
7.94093� 10�23 CC3 Cos�� Sin��3 �4.92704� 10�11 CC3 Cos�� Sin��3
A�
1.03169� 10�8 A CC3 Cos�� Sin��3 � 2.57923� 10�9 CC4 Cos�� Sin��3 �
3.59468� 10�11 A2 Cos��2 Sin��3 � 1.49367� 10�9 A4 Cos��2 Sin��3 �
1.07841� 10�10 A CC Cos��2 Sin��3 � 5.29396� 10�23 A2 CC Cos��2 Sin��3 �
Função a e b para o satélite MP 2.nb 5
5.97468� 10�9 A3 CC Cos��2 Sin��3 � 1.07841� 10�10 CC2 Cos��2 Sin��3 �
5.29396� 10�23 A CC2 Cos��2 Sin��3 � 8.96202� 10�9 A2 CC2 Cos��2 Sin��3 �
3.59468� 10�11 CC3 Cos��2 Sin��3
A� 5.97468� 10�9 A CC3 Cos��2 Sin��3 �
1.49367� 10�9 CC4 Cos��2 Sin��3 � 3.2381� 10�11 A2 Cos��3 Sin��3 �
1.32349� 10�23 A3 Cos��3 Sin��3 � 4.63875� 10�10 A4 Cos��3 Sin��3 �
9.7143� 10�11 A CC Cos��3 Sin��3 � 1.8555� 10�9 A3 CC Cos��3 Sin��3 �
9.7143� 10�11 CC2 Cos��3 Sin��3 � 2.78325� 10�9 A2 CC2 Cos��3 Sin��3 �
1.32349� 10�23 CC3 Cos��3 Sin��3 �3.2381� 10�11 CC3 Cos��3 Sin��3
A�
1.8555� 10�9 A CC3 Cos��3 Sin��3 � 4.63875� 10�10 CC4 Cos��3 Sin��3 �
1.03398� 10�25 A Sin��4 � 0.0000432135 A2 Sin��4 � 2.64698� 10�23 A3 Sin��4 �
7.49012� 10�10 A4 Sin��4 � 2.06795� 10�25 CC Sin��4 � 0.000086427 A CC Sin��4 �
1.58819� 10�22 A2 CC Sin��4 � 2.99605� 10�9 A3 CC Sin��4 � 0.0000432135CC2 Sin��4 �
1.03398� 10�25 CC2 Sin��4
A� 1.58819� 10�22 A CC2 Sin��4 � 4.49407� 10�9 A2 CC2 Sin��4 �
2.64698� 10�23 CC3 Sin��4 �7.92145� 10�12 CC3 Sin��4
A� 2.99605� 10�9 A CC3 Sin��4 �
7.49012� 10�10 CC4 Sin��4 � 4.33721� 10�12 A2 Cos�� Sin��4 � 5.29396� 10�23 A3 Cos�� Sin��4 �
1.43611� 10�9 A4 Cos�� Sin��4 � 1.30116� 10�11 A CC Cos�� Sin��4 �
1.05879� 10�22 A2 CC Cos�� Sin��4 � 5.74443� 10�9 A3 CC Cos�� Sin��4 �
1.30116� 10�11 CC2 Cos�� Sin��4 � 8.61665� 10�9 A2 CC2 Cos�� Sin��4 �
5.29396� 10�23 CC3 Cos�� Sin��4 �4.33721� 10�12 CC3 Cos�� Sin��4
A�
5.74443� 10�9 A CC3 Cos�� Sin��4 � 1.43611� 10�9 CC4 Cos�� Sin��4 �
2.14118� 10�11 A2 Cos��2 Sin��4 � 1.32349� 10�23 A3 Cos��2 Sin��4 �
2.40248� 10�9 A4 Cos��2 Sin��4 � 6.42355� 10�11 A CC Cos��2 Sin��4 �
2.64698� 10�23 A2 CC Cos��2 Sin��4 � 9.60991� 10�9 A3 CC Cos��2 Sin��4 �
6.42355� 10�11 CC2 Cos��2 Sin��4 � 2.64698� 10�23 A CC2 Cos��2 Sin��4 �
1.44149� 10�8 A2 CC2 Cos��2 Sin��4 � 1.32349� 10�23 CC3 Cos��2 Sin��4 �
2.14118� 10�11 CC3 Cos��2 Sin��4
A� 9.60991� 10�9 A CC3 Cos��2 Sin��4 �
2.40248� 10�9 CC4 Cos��2 Sin��4 � 1.61843� 10�12 A4 Cos��3 Sin��4 �
6.47374� 10�12 A3 CC Cos��3 Sin��4 � 9.71061� 10�12 A2 CC2 Cos��3 Sin��4 �
6.47374� 10�12 A CC3 Cos��3 Sin��4 � 1.61843� 10�12 CC4 Cos��3 Sin��4 �
4.68168� 10�10 A4 Cos��4 Sin��4 � 1.87267� 10�9 A3 CC Cos��4 Sin��4 �
2.80901� 10�9 A2 CC2 Cos��4 Sin��4 � 1.87267� 10�9 A CC3 Cos��4 Sin��4 �
4.68168� 10�10 CC4 Cos��4 Sin��4 � 4.23704� 10�12 A2 Sin��5 � 3.77078� 10�10 A4 Sin��5 �
1.27111� 10�11 A CC Sin��5 � 1.05879� 10�22 A2 CC Sin��5 � 1.50831� 10�9 A3 CC Sin��5 �
1.27111� 10�11 CC2 Sin��5 � 1.05879� 10�22 A CC2 Sin��5 � 2.26247� 10�9 A2 CC2 Sin��5 �
4.23704� 10�12 CC3 Sin��5
A� 1.50831� 10�9 A CC3 Sin��5 � 3.77078� 10�10 CC4 Sin��5 �
6 Função a e b para o satélite MP 2.nb
1.65874� 10�11 A2 Cos�� Sin��5 � 1.32349� 10�23 A3 Cos�� Sin��5 �
2.22631� 10�9 A4 Cos�� Sin��5 � 4.97623� 10�11 A CC Cos�� Sin��5 �
7.94093� 10�23 A2 CC Cos�� Sin��5 � 8.90526� 10�9 A3 CC Cos�� Sin��5 �
4.97623� 10�11 CC2 Cos�� Sin��5 � 7.94093� 10�23 A CC2 Cos�� Sin��5 �
1.33579� 10�8 A2 CC2 Cos�� Sin��5 � 1.32349� 10�23 CC3 Cos�� Sin��5 �
1.65874� 10�11 CC3 Cos�� Sin��5
A� 8.90526� 10�9 A CC3 Cos�� Sin��5 �
2.22631� 10�9 CC4 Cos�� Sin��5 � 1.45452� 10�9 A4 Cos��2 Sin��5 �
5.81809� 10�9 A3 CC Cos��2 Sin��5 � 8.72713� 10�9 A2 CC2 Cos��2 Sin��5 �
5.81809� 10�9 A CC3 Cos��2 Sin��5 � 1.45452� 10�9 CC4 Cos��2 Sin��5 �
5.97336� 10�10 A4 Cos��3 Sin��5 � 2.38934� 10�9 A3 CC Cos��3 Sin��5 �
3.58402� 10�9 A2 CC2 Cos��3 Sin��5 � 2.38934� 10�9 A CC3 Cos��3 Sin��5 �
5.97336� 10�10 CC4 Cos��3 Sin��5 � 7.55209� 10�13 A2 Sin��6 � 5.01478� 10�24 A3 Sin��6 �
3.86272� 10�10 A4 Sin��6 � 2.26563� 10�12 A CC Sin��6 � 2.63664� 10�24 A2 CC Sin��6 �
1.54509� 10�9 A3 CC Sin��6 � 2.26563� 10�12 CC2 Sin��6 � 2.63664� 10�24 A CC2 Sin��6 �
2.31763� 10�9 A2 CC2 Sin��6 � 5.01478� 10�24 CC3 Sin��6 �7.55209� 10�13 CC3 Sin��6
A�
1.54509� 10�9 A CC3 Sin��6 � 3.86272� 10�10 CC4 Sin��6 � 6.78031� 10�10 A4 Cos�� Sin��6 �
2.71212� 10�9 A3 CC Cos�� Sin��6 � 4.06818� 10�9 A2 CC2 Cos�� Sin��6 �
2.71212� 10�9 A CC3 Cos�� Sin��6 � 6.78031� 10�10 CC4 Cos�� Sin��6 �
8.2031� 10�10 A4 Cos��2 Sin��6 � 3.28124� 10�9 A3 CC Cos��2 Sin��6 �
4.92186� 10�9 A2 CC2 Cos��2 Sin��6 � 3.28124� 10�9 A CC3 Cos��2 Sin��6 �
8.2031� 10�10 CC4 Cos��2 Sin��6 � 1.33511� 10�10 A4 Sin��7 � 5.34042� 10�10 A3 CC Sin��7 �
8.01063� 10�10 A2 CC2 Sin��7 � 5.34042� 10�10 A CC3 Sin��7 � 1.33511� 10�10 CC4 Sin��7 �
5.9621� 10�10 A4 Cos�� Sin��7 � 2.38484� 10�9 A3 CC Cos�� Sin��7 �
3.57726� 10�9 A2 CC2 Cos�� Sin��7 � 2.38484� 10�9 A CC3 Cos�� Sin��7 �
5.9621� 10�10 CC4 Cos�� Sin��7 � 1.66397� 10�11 A4 Sin��8 � 6.65588� 10�11 A3 CC Sin��8 �
9.98382� 10�11 A2 CC2 Sin��8 � 6.65588� 10�11 A CC3 Sin��8 � 1.66397� 10�11 CC4 Sin��8
Função a e b para o satélite MP 2.nb 7
0.0 0.2 0.4 0.6 0.8 1.00.000
0.001
0.002
0.003
0.004
rad
Ckg
.km
2
Região 1
0.0 0.2 0.4 0.6 0.8 1.00.000
0.001
0.002
0.003
0.004
radC
kg.k
m2
Regiã o 2
0 .0 0 .2 0 .4 0 .6 0 .8 1 .00 .000
0.001
0.002
0.003
0.004
rad
Akg
.km
2
Reg ião 3
0.0 0 .2 0 .4 0 .6 0 .8 1 .00 .000
0.001
0.002
0.003
0.004
rad
Akg
.km
2
Reg ião 4
0.000 0.001 0.002 0.003 0.0040.000
0.001
0.002
0.003
0.004
0.005
A kg.km2
Ckg
.km
2
Região 5
0.000 0.001 0.002 0.003 0.0040.000
0.001
0.002
0.003
0.004
0.005
A kg.km2
Ckg
.km
2
Regiã o 6
0.001 0.002 0.003 0.004A kg.km2
5.0 101 8
1.0 101 9
1.5 101 9
2.0 101 9
2.5 101 9
D
0.00365 0.00370 0.00375 0.00380A kg.km2
2.0 101 5
4.0 101 5
6.0 101 5
8.0 101 5
1.0 101 6
1.2 101 6
1.4 101 6
D
0.001 0.002 0.003 0.004C kg.km2
2 101 8
4 101 8
6 101 8
8 101 8
1 101 9
D
0.0027 0.0028 0.0029 0.0030C kg.km2
2 101 6
4 101 6
6 101 6
8 101 6
D
0.0 0 .2 0 .4 0 .6 0 .8 1 .00
2 . 10 6
4 . 10 6
6 . 10 6
8 . 10 6
0 .00001
0.000012
rad
Ckg
.km
2
Reg ião 1
0.0 0 .2 0 .4 0 .6 0 .8 1 .00
2 . 10 6
4 . 10 6
6 . 10 6
8 . 10 6
0 .00001
0.000012
rad
Ckg
.km
2
Reg ião 2
0 5. 10 6 0.00001 0.0000150
2. 10 6
4. 10 6
6. 10 6
8. 10 6
0.00001
0.000012
A kg.km2
Ckg
.km
2
Regiã o 5
0 5. 10 6 0.00001 0.0000150
2. 10 6
4. 10 6
6. 10 6
8. 10 6
0.00001
0.000012
A kg.km2
Ckg
.km
2
Regiã o 6
0.0 0 .2 0 .4 0 .6 0 .8 1 .00
2 . 10 6
4 . 10 6
6 . 10 6
8 . 10 6
0 .00001
0.000012
rad
Akg
.km
2
Reg ião 3
0.0 0 .2 0 .4 0 .6 0 .8 1 .00
2 . 10 6
4 . 10 6
6 . 10 6
8 . 10 6
0 .00001
0.000012
rad
Akg
.km
2
Reg ião 4
0.0 0.2 0.4 0.6 0.8 1.0rad
5.0 103 3
1.0 103 4
1.5 103 4
2.0 103 4
2.5 103 4
3.0 103 4
3.5 103 4D
0 5. 10 6 0.00001 0.000015C kg.km2
2.0 103 5
4.0 103 5
6.0 103 5
8.0 103 5
1.0 103 6
1.2 103 6D
5. 10 6 0.00001 0.000015A kg.km2
5.0 103 5
1.0 103 6
1.5 103 6
2.0 103 6
D
0.0 0 .2 0 .4 0 .6 0 .8 1 .00 .000
0.001
0.002
0.003
0.004
rad
Ckg
.km
2
Reg ião 1
0.0 0 .2 0 .4 0 .6 0 .8 1 .00 .000
0.001
0.002
0.003
0.004
rad
Ckg
.km
2
Reg ião 2
0.0 0 .2 0 .4 0 .6 0 .8 1 .00 .000
0.001
0.002
0.003
0.004
rad
Akg
.km
2
Reg ião 3
0.0 0 .2 0 .4 0 .6 0 .8 1 .00 .000
0.001
0.002
0.003
0.004
radA
kg.k
m2
Reg ião 4
0.000 0.001 0.002 0.003 0.0040.000
0.001
0.002
0.003
0.004
0.005
A kg.km2
Ckg
.km
2
Reg ião 5
0.000 0.001 0.002 0.003 0.0040.000
0.001
0.002
0.003
0.004
0.005
A kg.km2
Ckg
.km
2
Reg ião 6