19890005752 NASA ( płaska ziemia ).pdf

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NASA
Reference
Publication
1207
1988
Derivation
and Definition
of a Linear Aircraft
Model
Eugene
L.
Duke,
Robert
F. Antoniewicz,
and Keith D. Krambeer
Ames
Dryden
Edwards,
Research
Flight
Center
Research
Facility
California
National Aeronautics
and
Space Administration
Scientific and Technical
Information Division
CONTENTS
SUMMARY
INTRODUCTION
SYMBOLS
Vectors
Matrices
S ubscripts
Superscript
NONLINEAR
1.1
1.2
Definition
..................................................
..................................................
.................................................
................................................
SYSTEM
of Reference
EQUATIONS
Systems
..................................
2
,1
d
5
5
5
6
ll
11
1-1
15
16
17
1S
20
20
21
21
.............................
vehicle
center
of gravity
.................
...........................
21
21
22
22
................................
Equation
System
Matrices
............................
Equations
.....................
...........................
23
24
26
27
30
31
FORCES
OF
V,
THE
&, AND
AND
WIND
_
......................................
.....................................
.....................................
.....................................
MOMENTS
AXIS
TRANSLATIONAL
35
35
35
36
37
31
Nonlinear
State
1.2.1
Rotational
1.2.2
1.2.3
1.2.4
Translational
Attitude
Equations
.....................................
acceleration
...................................
acceleration
rates
..................................
........................................
velocity
....................................
.................................
Equations
Earth-relative
Observation
Accelerations
Air
data
1.3
Nonlinear
1.3.1
1.3.2
1.3.3
1.3.4
1.3.5
1.3.6
1.3.7
1.3.8
.........................................
parameters
.....................................
parameters
parameters
rates
and
...............................
.................................
Flightpath-related
Energy-related
Force
Body
parameters
axis
......................................
accelerations
from
the
Instruments
Miscellaneous
SYSTEM
displaced
observation
EQUATIONS
parameters
LINEAR
2.1
2.2
2.3
2.4
3
Linearization
Linearization
Definition
Elements
of the
of the
of Matrices
of the
State
Equation
Observation
in Linearized
System
Linearized
CONCLUDING
REMARKS
APPENDIXES
A--AERODYNAMIC
B--DERIVATION
PARAMETERS
B.1
B.2
B.3
B..I
Preliminary
Derivation
Derivation
Derivation
Definitions
of I}" Equation
of 5
of/)
Equation
Equation
iii
PRECEDING
PAG_
RLANg
N_
FILMED
C--GENERALIZED
C.1
C.2
Generalized
Generalized
DERIVATIVES
Derivatives
Derivatives
OF
of the Time Derivatives
of State Variables
of the Observation
Variables
......................
..............
39
39
,'13
49
49
49
50
50
51
51
52
53
53
5,'t
55
56
57
°
D--EVALUATION
D.1
DERIVATIVES
......................................
derivatives .................................
Preliminary
Evaluation
D.I.1
Rolling moment
D.1.2
D.1,3
D.1.4
D.1.5
D.1.6
Pitching
moment derivatives ................................
Yawing moment derivatives .................................
Drag force derivatives ....................................
Sideforce
derivatives
.....................................
Lift force derivatives .....................................
_
D.2
Evaluation
of the Derivatives
of the Time Derivatives
of the State Variables
........................................
D.2.1
D.2.2
D.2.3
D.2.4
D.2.5
D.2.6
D.2.7
D.2.8
D.2.9
D.2.10
D.2.11
D.2.12
D.2.13
Roll acceleration
Pitch acceleration
Yaw acceleration
Decoupled
derivatives ................................
derivatives ................................
derivatives
................................
derivatives
...........................
roll acceleration
Decoupled
pitch acceleration
derivatives ..........................
Decoupled
yaw acceleration
derivatives ..........................
Total vehicle acceleration
derivatives ...........................
Angle-of-attack
rate derivatives ..............................
Angle-of-sideslip
rate derivatives ..............................
Roll attitude
rate derivatives ................................
Pitch attitude
rate derivatives ...............................
IIeading
Altitude
rate
rate
derivatives
derivatives
..................................
..................................
57 1
58
59
60
62
62
63
64
65
65
...................
66-
66
67
:
68
69
69
70
71
center
72
1
D,3
D.2.14 North acceleration
derivatives ...............................
D.2.15 East acceleration
derivatives ................................
Evaluation
of the Derivatives
of the Observation
Variables
D.3.1
D .3.2
D.3.3
D .3.4
D.3.5
D .3.6
D.3.7
D .3.8
D.3.9
D.3.10
D.3.11
D.3.12
D.3.13
D.3.14
Longitudinal
kinematic
acceleration
derivatives ......................
Lateral kinematic
acceleration
derivatives .........................
Z-body
x body
axis kinematic
acceleration
axis accelerometer
output
derivatives ......................
derivatives .......................
y body axis accelerometer
output derivatives .......................
z body axis accelerometer
output derivatives .......................
Normal accelerometer
output
derivatives .........................
Derivatives
of x body axis accelerometer
output not at the vehicle
of gravity ...........................................
Derivatives
of y body axis accelerometer
of gravity ...........................................
Derivatives
of z body axis accelerometer
of gravity ...........................................
Derivatives
of normal accelerometer
output
output
not at vehicle
not at vehicle
center
72
center
73
output
not at vehicle
center
74
75
76
77
of gravity ...........................................
Load factor derivatives ...................................
Speed of sound derivatives .................................
Mach number derivatives ..................................
iV
D.3.15
D.3.16
D.3.17
D.3.18
D.3.19
D .3.20
D.3.21
D.3.22
D.3.23
D.3.24
D.3.25
D.3.26
D.3.27
D.3.28
D.3.29
D.3.30
D.3.31
D.3.32
D.3.33
D.3.34
D.3.35
D.3.36
D.3.37
D.3.38
D.3.39
D.3.40
D.3.41
REFERENCES
Reynolds
Reynolds
Dynamic
number
number
pressure
derivatives ................................
per unit length derivatives .......................
derivatives ................................
77
78
79
80
81
82
82
83
84
85
86
87
87
. .........
88
89
90
90
91
92
93
93
9-t
95
96
97
97
98
101
hnpact
pressure derivatives .................................
Mach meter calibration
ratio derivatives ..........................
Total temperature
Flightpath
angle
derivatives ...............................
derivatives ................................
Flightpath
acceleration
derivatives .............................
Vertical acceleration
derivatives ..............................
Specific
Specific
Normal
Axial
x body
y body
z body
x body
y body
energy
derivatives
.................................
power derivatives ..................................
force derivatives ..................................
force derivatives
axis rate
....................................
........................
.................................
.................................
............................
............................
derivatives
axis rate derivatives
axis rate derivatives
axis acceleration
axis acceleration
derivatives
derivatives
z body axis acceleration
derivatives ............................
Angle-of-attack
sensor output derivatives .........................
Angle-of-sideslip
sensor output derivatives ........................
Altimeter
output
derivatives ................................
Altitude
rate sensor output derivatives ..........................
Total angular momentum
derivatives ...........................
Stability
axis roll rate derivatives .............................
Stability
axis pitch rate derivatives ............................
Stability
axis yaw rate
derivatives
.............................
V

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