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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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L12

L221 �

L3

L21 �

L32

L22Sin�h � 2 l2 � l3 Sin�2 � �

�1

2�

3 L12

2 L22�

3

41 �

L32

L22Sin�2 h � 2 l3 Sin��2 �

3 L3 1 � L32

L22Sin�h � l3 Sin�2 �

4 L2

D�F, L1� �

�1

2 A�

1

2 B�

1

CCL1 � �

1

A�

1

Bcos l1 L1 �

1

2 L6��A � B � 2 CC� M6 Μ4

3 �1 � 3 H2

G2� L12 L3 1 � L32

L22Cos�l2

4 1 � L12

L22L24

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

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3 L12

2 L22�

3 �1 � H

G�2

L32 Cos�2 g � 2 h � 2 l � 2 l3

8 L23�

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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

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4 L23�

1

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H

G

2

1 �L32

L22Cos�2 g � 2 h � 2 l � 2 l3 �

3

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1 �L32

L22

Cos�2 g � 2 h � 2 l � 2 l3 �3

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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�

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8 L22�

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L22�1 � L3

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4 L22�

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4 L22�

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8 L22�

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16 L22 1 � L32

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L22� 1 � L32

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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

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16 L2�

3 �1 � H

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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�

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8 L22�

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4 L22�

3 �1 � H

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L22� L3 �1 � L3

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16 L22 1 � L32

L22

3 �1 � H

G� �1 � L12

L22� 1 � L32

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16 L2�

9 �1 � L12

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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�

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L22� �1 � L3

L2� Cos�2 h � 2 l2 � 2 l3 Sin��2

16 L2�

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3 L12

2 L22

3 �1 � H

G�2

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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�

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L22�1 � L3

L2� Cos�h � l2 � l3 Sin�2 �

4 L22�

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L22�1 � 2 L3

L2� Cos�h � l2 � l3 Sin�2 �

8 L22�

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8 L22�

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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

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L22� 1 � L32

L22Cos�h � 2 l2 � l3 Sin�2 �

16 L2� �

1

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2 L22

3

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L22�

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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, �� �

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9.26759� 10�10 A3 CC � 0.0000303794CC2 �2.06795� 10�25 CC2

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2 Função a e b para o satélite MP 2.nb

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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

0.0 0.2 0.4 0.6 0.8 1.0rad

2 101 7

4 101 7

6 101 7

8 101 7

1 101 8D

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

0.2 0.4 0.6 0.8 1.0rad

0.5

0.6

0.7

0.8

D

0.001 0.002 0.003 0.004C kg.km2

100000

200000

300000

D

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010A kg.km2

500000

1.0 106

1.5 106

2.0 106

2.5 106

3.0 106D