Tesis Javeriana Serpentine
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Transcript of Tesis Javeriana Serpentine
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)
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∈{
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= + ( − 1) , = 1,2,…….,
( ) = = 1
( − 1) + ∈[2, ]
( ) = = 1
( − 1) + ∈[2, ]
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( ) ( ) ( )
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=
− 0 ∗
0 ∗
0 0 1 00 0 0 1
=
− 0 ∗
0 ∗
0 0 −1 00 0 0 1
=
− 0 ∗
0 ∗
0 0 1 00 0 0 1
=
− 0 ∗
0 ∗0 0 1 00 0 0 1
=
− 0 ∗
0 ∗
0 0 1 0
0 0 0 1
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=
− 0 ∗
0 ∗
0 0 1 0
0 0 0 1
= ∗ ∗ ∗ ∗ ∗
=
( ) − ( ) 0 + ( + ) + ( + + ) + ( )
( ) ( ) 0 + ( + ) + ( + + ) + ( )
0 0 1 0
0 0 0 1
= 2 1 + ( 1 + 2) + ( 1 + 2 + 3) + ( )
=2
1 + ( 1 + 2) + ( 1 + 2 + 3) + ( )
= + − 2 cos
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( + ) = + − 2 cos(180 − )
cos(180 − ) = −cos( )
cos( ) =
θ = / 2 =
θ = /
/
θ
= cos = cos( + )
= sin = sin( + )
= + = + = +
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+ ( + ) + ( + )
= ( + + 2 ) + + + 2
+ + 2 ( +
+ + + 2
.
= / 2 =
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Θ ̇ = ̇ ̇
= 2 1 + ( 1 + 2) + ( 1 + 2 + 3) + ( 1 + 2 + 3 + 4)
2 1 + ( 1 + 2) + ( 1 + 2 + 3) + ( 1 + 2 + 3 + 4)
Θ ̇ = (Θ) ̇
̇
(Θ) = − / 2sin − sin( + ) − sin( + )
/ 2cos + cos( + ) cos( + )
̇
̇= (Θ)
̇ ̇
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( ) = (0) =
=
(̇ ) = ̇ (0) = 0 ̇ = 0
( ) = + ( ∗ ) + ( ∗ ) + ( ∗ )
( ) = (0) → =
= + ∗ + ∗ + ∗ =
(̇ ) = + (2 ∗ ∗ ) + (3 ∗ ∗ )
(̇ ) = ̇ (0) = → = 0 (2.40)
̇ = 2 ∗ ∗ + 3 ∗ ∗ = 0 (2.41)
= = 0
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= ( )
= ( )
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