A Mathematical Model of a Single Main Rotor Helicopter for ... - Read

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APPENDIX I LINEARIZED SIX-DEGREE-OF-FREEDOM REPRESENTATION OF HELICOPTER DYNAMICS The linear , f irst-order set of differential equations describing the rigid body motion of the helicopter are of the form: 2 = [FIX + [GI6 yr where x represents the perturbations from trim of the state variables UB, WB, qBy 0, VB, PB, $I, and rB; and 6 represents the deviations from the trim control posi- The linear representation is valid only if the initial tions of 6,, 6,, 6,, and 6p. =- angular velocities p ~ qBy , and rB are zero. The elements of the F and G matrices are of two types. The first type consists of inertial and gravitational terms that can be obtained analytically from the equations of motion. The second type consists of partial derivatives arising from aerodynamic forces and moments. The force and moment derivatives are obtained by considering both position and negative perturbations from trim. For example: The elements of the F and G matrices and the state variable vectors are given in table 1-1. 39
a 8 a m a ma a 0 a m 0. a 3" a m a v E+ n a W 4 m W a U W a " W v 4 II II x w I I I I I I I I I I I I I I 40 h N N X Y I N H X H v II U H I I I I I I _- 7--r--- I I I I I I I I
Page 1 and 2: 1 \ 1 i I ! t ... NASA Technical Me
Page 3 and 4: I . I CONTENTS SuMMAEtY ...........
Page 5 and 6: 1 2 3 4 B- 1 B-2 D- 1 FIGURES Block
Page 7 and 8: 0 Q p 0 16 9 2 w a, U & 3 4 t4 0 U
Page 9 and 10: summing the contributions, to each
Page 11 and 12: sideslip that will be encountered a
Page 13 and 14: gust levels. For this representatio
Page 15 and 16: damping matrix in flapping differen
Page 17 and 18: 0 Euler pitch angle, rad 00 et A bl
Page 19 and 20: HU B-BODY AIRCRAFT REFERENCE SYSTEM
Page 21 and 22: 1w II 8 2 + - + w 0 N Nlm I n "w (N
Page 23 and 24: 18 c
Page 25 and 26: (-& Q = nb pacR2 (RR) [l + (1 - - (
Page 27 and 28: (B, is defined as zero if VH = UH =
Page 29 and 30: 1 + jJ KlTRblTR - a blm +-- 4 'TR T
Page 31 and 32: This implicit relationship is solve
Page 33 and 34: APPENDIX E EMPENNAGE FORCES AND MOM
Page 35 and 36: The angle iHs is the incidence of t
Page 37 and 38: APPENDIX F CALCULATION OF FUSELAGE
Page 39 and 40: The forces and moments in the body-
Page 41 and 42: It is important to note that the cu
Page 43: c, = ‘C, (s) The terms CK1 and CK
Page 47 and 48: TABLE J-1.- CONFIGURATION DESCRIPTI
Page 49 and 50: Fus pitch moment, a = B = 0 TABLE J
Page 51 and 52: REFERENCES l . 1 . Sinacori, J. B.;

A Mathematical Model of a Single Main Rotor Helicopter for ... - Read

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