Conventional airplane Linear differential equations - Longuitudinal Dynamics and Lateral Dynamics CDu C D u CD0 CD0 CDF W CPX u CPX 0 SF q S q S CD0 H H CD0 H V H V S q SW q SW CS A CS R C CD D CL0 Lift coefficient at zero AoA CD C CDq D q C CD D E E CD CS C S p CS CS p CS r C S A CSr CLu CPZ u CPZ 0 CS R CL u CL R CL R CM u moment cofficient at zero AoA CM u CL CL CL CL CL CLq q CL CL E E CL CL p CL CLr r CL CL A A CLp CL CM 0 CPM u CPM 0 CM CM P CM C CM M C CM q M q C CM M E E C N CN C N CN p p C N CNr r C N C N A A C N R C N R bW main wing span I xx y 2 z 2 V dV 2 z 2 V dV q dynamic pressure y 2 V dV m vehicle ' s mass Vol I yy x Vol I zz x 2 cW mean chord length SW main wing area 0 zero lift angle of attack Vol I xy I yx xy V dV V dV U 0 trim reference velocity at x axis Vol I xz I zx xz Vol I yz I zy yz V dV Vol dT xT acW XF acH X Re f T xT V T T dT Dynamics properies m u Q0 w W0 q V0 r R0 v mg cos 0 f AX f PX m v R0 u U 0 r P0 w W0 p mg cos 0 cos 0 sin 0 sin 0 f AY f PY m w P0 v V0 p Q0 u U 0 q mg cos 0 sin 0 sin 0 cos 0 f AZ f PZ u Q0 w W0 q V0 r R0 v g cos 0 f AX f PX / m cos f /m v R0 u U 0 r P0 w W0 p g cos 0 cos 0 sin 0 sin 0 f AY f PY / m w P0 v V0 p Q0 u U 0 q g cos 0 sin 0 sin 0 f AX f PX m f AY f PY m f AZ f PZ m f AX f PX f AY m f PY m f AZ f PZ m q SW m 0 AZ f PZ 2 2 CD0 CPX CPX CDu u 0 U U 0 0 T cos T 0 u CD CL0 CD CDq q CD E E m q SW CS CS p p CSr r CS A CS R A R m T sin T 0 q S 2 2 W CLu CL0 CPZ CPZ u CL CD0 CL CLq q CL E u 0 E m U0 U0 m X u u X Pu u X X X q q X E E X T T Y YP P Yr r Y A A Y R R Z u u Z Pu u Z Z Z q q Z E E ZT T mA mP / I yy Dynamics properies p I xz 1 r I xz Q0 p P0 q I yy I zz R0 q Q0 r l A lP I xx I xx q 1 I yy r I xz 1 p I xz R0 q Q0 r I xx I yy Q0 p P0 q n A nP I zz I zz q 1 I yy I zz I xx R0 r P0 r 2 I xz R0 r P0 p m A mP I zz 1 1 I 2 xz I xz 1 I xx I zz I zz I xx R0 r P0 r 2 I xz R0 r P0 p m A mP 1 p 1 2 r I I xz 1 xz I xx I zz I zz I xz 1 I xz Q0 p P0 q I yy I zz R0 q Q0 r l A lP I xx I xx 1 I xz R0 q Q0 r I xx I yy Q0 p P0 q n A nP 1 I zz mA mP q SW cW I yy I yy 2 2 CM 0 CPM CP CM u u U0 U 0 M0 L' L N I xz / I xx D L'p L p N p I xz / I xx D ' Lr Lr N r I xz / I xx D ' L A L A N A I xz / I xx D ' L R L R N R I xz / I xx D ' ' ' ' ' L L p p L r r L A A L R R ' ' ' ' ' N N p p N r r N A A N R R N ' N L I xz / I zz D N p' N p L p I xz / I zz D 1 N r' N r Lr I xz / I zz D D I xz2 ' 1 N A N A L A I xz / I zz D I xx I zz ' N R N R L R I xz / I zz D dT cos T xT sin T u CM CM P CM CM q q CM E E T I yy nA nP q SW bW C N C N p p C N r r C N A C N R A R I zz I zz l A lP L L p p Lr r L A A L R R I xx mA mP M u u M Pu u M M P M M q q M E E M T T I yy nA nP N N p p N r r N A A N R R I zz I xz I xx l A l p / I xx nA nP / I zz 1 l A lP q SW bW CL CLp p CLr r CL A CL R A R I xx I xx M u u M Pu u M M P M M q q M E E M T T p tan 0 sin 0 q cos 0 r Q0 cos 0 R0 sin 0 Q0 sin 0 R0 cos 0 0 sin 0 tan 0 cos 0 q sin 0 r Q0 sin 0 R0 cos 0 0 tan 0 sin 0 q cos 0 r R0 sin 0 Q0 cos 0 / cos 0 Dynamics properies at level flight w Z u u Z Pu u Z Z Z q U 0 q Z E E ZT T u g f AX f PX / m v U 0 r g f AY f PY / m u g X u u X Pu u X X X q q X E E X T T q M u u M Pu u M M M q q M E E M T T w U 0 q f AZ f PZ / m q u g X u u X Pu u X X X q q X E E X T T v g Y YP P Yr U 0 r Y A A Y R R v g Y YP P Yr U 0 r Y A A Y R R w Z u u Z Pu u Z Z Z q U 0 q Z E E ZT T q mA mP / I yy p 1 2 r I xx I zz I xz I zz I xz I xz l A lP I xx nA nP p L' L' p p L'r r L' A A L' R R q M u u M Pu u M M P M M q q M E E M T T r N ' N ' p p N 'r r N ' A A N ' R R p L' L' p p L'r r L' A A L' R R r N ' N ' p p N 'r r N ' A A N ' R R p u g X u u X Pu u X X X q q X E E X T T w Z u u Z Pu u Z Z Z q U 0 q Z E E ZT T q M u u M Pu u M M M q q M E E M T T q 1 Z u Z Pu u Z Z q U 0 q Z E E ZT T U Z 0 X Z u Z Pu u X u X Pu U 0 Z u X X Z U 0 Z U0 Zq g X q X U 0 Z 1 Z u u Z Pu u Z Z q U 0 q Z E E ZT T U 0 Z M Z u Z Pu q M u M Pu U 0 Z q h w U 0 w U 0 u M M P M Z U 0 Z X Z E q X E U 0 Z X ZT E XT U 0 Z T M q M U0 Zq U 0 Z M Z E q M E U 0 Z M ZT E MT U 0 Z T X Z Z Pu Xu X P u u U 0 Z Z u Z Pu U 0 Z A 0 M Z Z Pu M M u Pu u U 0 Z 0 X Z E X E U 0 Z Z E U 0 Z B 0 M M Z E E U 0 Z 0 X Z X U 0 Z Z U 0 Z 0 g 0 0 M Z M M P 0 U 0 Z U 0 U0 X ZT XT U 0 Z ZT U 0 Z 0 M ZT MT U 0 Z 0 1 0 0 , C 0 0 X q X U0 Zq U 0 Z U0 Zq U 0 Z 1 M q M 0 0 0 0 0 0 1 0 0 0 0 1 0 0 , D 0 0 0 1 0 0 0 0 0 0 1 U0 Zq U 0 Z 0 0 0 0 0 0 0 0 0 0 0 u x y , u E T q h v g Y YP P Yr U 0 r Y A A Y R R p L' L' p p L'r r L' A A L' R R x y p, u A R r r N ' N ' p p N 'r r N ' A A N ' R R p Y Y Yp Y Y g p r 1 r A A R R U0 U0 U0 U0 U0 U0 0 tan 0 sin 0 q cos 0 r R0 sin 0 Q0 cos 0 / cos 0 Y U 0 0 A ' L N ' 0 Yp g U0 U0 0 1 0 L'p 0 N p' 0 0 Y A Yr 1 0 U0 U0 0 0 0 ' B L'r 0 L A N ' N r' 0 A 0 1 0 Y R 1 U0 0 0 0 C L' R ' 0 N R 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 D 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0