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

Planetary Exploration Using Biomimetics
An Entomopter for Flight on Mars
Cpθhc φ
() := −2
⋅ π⋅
⎡
⎢
⎣
⎛
⎜
⎝
Gα() φ + k() φ ⋅ Fα φ
()
+
1
2
⎞⎤ ⎥⎦
⎠
Cpθhs() φ := 2 ⋅ π ⋅
⎡
⎢
⎣
−
Fα()
φ
+
k() φ ⋅ Gα φ
()
+
⎛
⎜
⎝
k() φ
2
2
⎞⎤
⎥
⎠⎦
Cphh0() φ := 4 ⋅ π ⋅
Fh()
φ
Cphhc φ
():=
−4
⋅ π⋅
Cphhs () φ := 2 ⋅ π ⋅
Fh()
φ
( ())
k() φ + 2⋅
Gh φ
Cpθ0hs φ
():=
−4
⋅
π
ψθh() φ := atan
⎡
⎢
⎢
⎣
−Fα()
φ
+ k() φ ⋅ Gα()
φ
⎛
⎜
⎝
Gα() φ + k() φ ⋅ Fα φ
()
+
1
2
⎤ ⎥⎥⎦
⎞
⎠
( ) := Clθ0() φ ⋅ α0()
t + ( Clθc( φ) ⋅ cos( ω ⋅ t + φα()
t ) + Clθs () φ ⋅ sin( ω ⋅ t + φα()
t )) ⋅ α1 t
k()
φ
+ ( Clhc() φ ⋅ cos( ω ⋅ t + φht ())
+ Clhs() φ ⋅ sin( ω ⋅ t + φht ()))
⋅ ⋅ h1()
t
2⋅
b()
φ
Cl φ,
t
( ) := ( Cmθc () φ ⋅ cos ( ω ⋅ t + φα()
t ) + Cmθs () φ ⋅ sin( ω ⋅ t + φα()
t )) ⋅ k()
φ
h1()
t
+ Cmh() φ ⋅ cos ( ω ⋅ t + φht ())
⋅ k()
φ ⋅
()
Cm φ,
t
2⋅
b φ
⋅
()...
α1t ()
...
( ) := ( Ctθθ0() φ + Ctθθc() φ ⋅ cos ( 2 ⋅ ω ⋅ t + 2 ⋅ φα()
t ) + Ctθθs() φ ⋅ sin( 2 ⋅ ω ⋅ t + 2 ⋅ φα()
t )) ⋅ α1 t
Ct φ,
t
2
Ctθh0() φ ⋅ cos ( φh() t − φα()
t − φhθ()
φ)
⎛ k() φ ⋅ h1()
t ⎞
+
... ⎞ ⋅ α0()
t ⋅ ⎜
...
+ Ctθhc() φ ⋅ cos ( 2 ⋅ ω ⋅ t + φα()
t + φht ())
... ⎝ 2⋅
b()
φ ⎠
+ Ctθhs() φ ⋅ sin( 2 ⋅ ω ⋅ t + φα()
t + φht ())
⎠
+ Cthh0() φ + Cthhc() φ ⋅ cos( 2 ⋅ ω ⋅ t + φα()
t ) + Cthhs() φ ⋅ sin( ω ⋅ t + φα()
t )
+ Ctθ0hc() φ ⋅ cos( ω ⋅ t + φht ())
+ Ctθ0hs() φ ⋅ sin( ω ⋅ t + φht ())
⋅ () ⋅ k φ
⎛
⎜
⎜
⎝
( ) ⋅ α0()
t ⋅
h1()
t
( ) α0 t () ⋅
2⋅
b()
φ
() 2 ...
α1t ()
...
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Phase II Final Report