State Space Basics State space models are of the form x()= Ax(t)+ Bult) y(t)= Cx(t)+ Dult) with associated transfer function G()=C(sI-A)

Matrix Diagonalization Suppose a is diagonizable with independent eigenvectors use similarity transformations to diagonalize dynamics matrix

mu Xuu+ Xww-mg cos 000+ m(wi-qUo) Zuu+ Zww Ziw+ Zgq-mg sin+ Iyyq Muu+ Mww+ Mww+ Mq+ There is no roll/yaw motion, so=0. Control commands△x,△z,and△ MC have not yet been specified

Note can develop good approximation of key aircraft motion(Phugoid) using simple balance between kinetic and potential energies. Consider an aircraft in steady, level flight with speed U and height ho. The motion is perturbed slightly so that

For general applications in 3D, often need to perform 3 separate rotations to relate our inertial frame to our body frame Especially true for aircraft problems There are many ways to do this set of rotations -with the variations be based on the order of the rotations All would be acceptable

Static stability is all about the initial tendency of a body to return to its equilibrium state after being disturbed To have a statically stable equilibrium point, the vehicle must develop a restoring force/ moment to bring it back to the eq. condition Later on we will also deal with dynamic stability, which is concerned with the time history of the motion after the disturbance

Aircraft Performance Accelerated horizontal flight-balance of forces -Engine thrust TLift(toV)

一、回顾FEM和F一D 二、一维实例 三、一二三维的有限差分矩阵 四、高斯消元的代价 五、Krylov法 六、通讯下限 七、基于改善通讯的预条件器

一、积分方程法 二、外部与内部问题 三、应用点源开始 四、二维标准解法 五、Galerkin法 六、配置法 七、三维形式 八、板积分

一、离散化积分方程的求解 二、应用 Krylov子空间法 三、快速矩阵向量积 四、多极点算法 五、多极点表示 六、基本层次 七、算法改善 八、局部展开