tailieunhanh - Aeronautical Engineer Data Book Episode 7

Tham khảo tài liệu 'aeronautical engineer data book episode 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Principles of flight dynamics 111 Moments of inertia Ix Y8m y2 z2 Moment of inertia about Ox axis Iy Zỗm x2 z2 Moment of inertia about Iz Zỗm x2 y2 Oy axis Moment of inertia about Oz axis Ixy Eỗm xy Product of inertia about Ox and Oy axes Ixz Eỗm xz Product of inertia about Ox and Oz axes Iyz Eỗm yz Product of inertia about Oy and Oz axes The simplified moment equations become ỊP - Iy - Iz qr -1 pq r L_ IẠ - Ix - Iz Pr - Ixz p2 - r2 M Izr - Ix- Iy pq - Ixz qr p N J Non-linear equations of motion The generalized motion of an aircraft can be expressed by the following set of non-linear equations of motion m U - rV qW Xa Xg Xc Xp Xd m V- pW rU Ya Yg Y_c Yp Yd m W - qU pV Za Zg Zc Zp Zd Ixp - Ị - Ix qr - Ixz pq r La Lg Lc Lp Ld Iyq Ix - Iz pr Ixz p - Y Ma Mg Mc Mp Md zr - Ix- Iy pq Ixz qr - p Na Ng Nc Np Nd The linearized equations of motion In order to use them for practical analysis the equations of motions are expressed in their linearized form by using the assumption that all perturbations of an aircraft are small and about the steady trim condition. Hence the equations become 112 Aeronautical Engineer s Data Book m u qWe Xa Xg X Xp m v PWỉ rU Ya Yg Yc Yp m w qUe Za Zg Zc Zp Ixp - Xz r La Lg Lc Lp Iy q Ma Mg Mc Mp X r - Ixz p Na Ng Nc Np A better analysis is obtained by substituting appropriate expressions for aerodynamic gravitational control and thrust terms. This gives a set of six simultaneous linear differential equations which describe the transient response of an aircraft to small disturbances about its trim condition . mu - XX uu - XX v v - XX w w - XX w w -XX p p - XXq - mWe q - XXrr mgq cos e X X q X X Tr -Yu u mv - Yv v - Yw w - Yw w Yp mWpp -Yq q - Yr - mUX r - mg b cosỡe - mgp sinỡe Y Ềx Y lị Y Y Tr -Z u u - Z v v m - Z w w w - Z w w -Zp p - Zq -mUt t - Zrr mgd sinỡe ịX Z Z Ị Ị Z t7 -L uu - í v - L-K w - J-w w Ix p - Lp p - Lq q - Ixz r - Lr r L-Z X ỉ-z V Lsỉ Lp -Mí u u - Mí v v - Mỉ w w -Mw w - Mp p Iy q - Mq q - Mr r M ị X Mí Mí Mí tT -Nu