Phase II Final Report - NASA's Institute for Advanced Concepts

Planetary Exploration Using Biomimetics
An Entomopter for Flight on Mars
( () 2 + Fα()
φ)
⎣ + ⎡⎣ ( () ()) ( 1 − 2⋅
Fαφ ())
⎤⎦
Ctθθc() φ := π ⋅ ⎡ k() φ
2 ⋅ Gαφ () 2 − Fαφ
⎢
2⋅
k φ ⋅ Gα φ ⋅
() 2
() 2
+ Fα φ − Gα φ
−
Fα()
φ
...
⎤ ⎥⎦
Ctθθs() φ := π ⋅ ⎡ Gα() φ ⋅ ( 1 − 2⋅
Fαφ ())
...
⎢
+ k() φ ⋅ ⎛ 2⋅
Gαφ () 2
− 2⋅
Fαφ
⎜
1
⎜ + 2⋅
Fαφ () +
2
⎢
⎢
⎣
Ctθh0() φ := 2 ⋅ π ⋅
⎡
⎢
⎣
⎝
⎛
⎜
⎝
() 2
...
⎞
⎠
+ k() φ
2 ⋅ Gαφ () ⋅
( () )
2⋅ Fαφ − 1
Gh() φ k() φ 2⋅
Fh() φ
2
+ 2⋅
Gh() φ
2 1
+ ⋅
− Fh()
φ +
2
+ ( 2⋅
Fh() φ
2
+ 2⋅
Gh() φ
2
− Fh()
φ − k() φ ⋅ Gh()
φ ) 2
2
⎞⎤ ⎥⎦
⎠
...
⎤ ⎥
⎥
⎥
⎦
Ctθhc() φ := 2 ⋅ π ⋅
⎡
⎢
⎣
Gh() φ ⋅ 1 − 4⋅
Fh φ
( ())
+
⎛
⎜
⎝
k() φ ⋅ 2⋅
Gh φ
() 2
−
2⋅
Fh() φ
2
+
Fh()
φ
+
1
2
⎞⎤
⎥
⎠⎦
Ctθhs () φ := 2 ⋅ π ⋅ 2⋅ Gh() φ
2
− 2⋅
Fh φ
Cthh0() φ := 4 ⋅ π ⋅
Cthhc() φ := 4 ⋅ π ⋅
⎡⎣
Cthhs () φ := 8 ⋅ π ⋅
Ctθ0hc() φ := 2 ⋅ π ⋅
Ctθ0hs φ
() := −4
φhθ() φ := atan
⎡
⎢
⎢
⎣
( Fα() φ
2 − Gαφ () 2 )
( Gα() φ
2 − Fαφ () 2 )
⋅ π⋅
Fα()
φ
⋅
Gα()
φ
k() φ − 2⋅
Gh φ
() 2
( ())
Fh()
φ
+ Fh()
φ + k() φ ⋅ Gh()
φ ⋅ 4⋅ Fh()
φ − 1
(
( Fh() φ − 2⋅
Fh() φ
2 − 2⋅
Gh() φ
2 + k() φ ⋅ Gh()
φ )
⎛
⎜
⎝
Gh() φ + k() φ ⋅ 2⋅ Fh() φ
2 + 2⋅
Gh() φ
2 − Fh φ
()
( ) ⎤ ⎦
+
1
2
⎤
⎥⎥⎦
⎞
⎠
Clθ0() φ := 2 ⋅ π
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Phase II Final Report