tailieunhanh - Aerospace Technologies Advancements Fig Part 3

Tham khảo tài liệu 'aerospace technologies advancements fig part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 60 Aerospace Technologies Advancements Fig. 2. Configuration of Flexible Spacecraft X 7Flexible Solar Array Spacecraft M sin E ody Fleadbls Solar Array Fig. 3. Dynamic Model of Flexible Spacecraft Spacecraft Attitude Control 61 By having M value of the point mass L distance of the point mass from the spacecraft center of mass If moment of inertia of the movable material frame with respect to the x-axis the moments of inertia of the undeformed spacecraft are Ixx Ix 2If 41 Iyy Iy 2ML2 42-a Izz Iz 2ML2 42-b where Ix Iy and Iz are the principal moments of inertia of the rigid body. Assuming small deflections rotations of the appendages . ay . px small . Also assuming that the spacecraft main body angular velocity components referred to the principal axes of inertia fíx fíy and fíz are very small therefore neglecting their products. Then the dynamics of the flexible spacecraft become Lorenzo 1975 Ixx x t If x t x t Tx t 43-a Vy t ML z t - -z t Ty t 43-b Izz z t ML y t - y t Tz t 43-c x t t ax t - x t 43-d x t TỷPx t Px t - x t 43-e y t j-y t ay t - - z t L 43-f y t y t Py t t L 43-g z t - -z t 7paz t .y t L 43-h z t - z t Pz t - . .y t L 43-i where Tx t Ty t . and Tz t are the torques applied to the spacecraft main body. Moreover if fx ax Px fy tty Py fz az pz the dynamics of the flexible spacecraft are described by the following decoupled set of equations Lorenzo 1975 Ixx x t Ifx t Tx t 44-a