Aircraft Lateral dynamics Using a procedure similar to the longitudinal case, we can develop the equations of motion for the lateral dynamics

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

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

美国麻省理工大学：《Aerospace Dynamics（航空动力学）》英文版 lecture 11

Spring 2003 Derivation of lagrangian equations Basic Concept: Virtual Work Consider system of N particles located at(, x2, x,,.x3N )with 3 forces per particle(f. f, f..fn). each in the positive direction

Spring 2003 Example Given: Catapult rotating at a constant rate(frictionless, in the horizontal plane) Find the eom of the particle as it leaves the tube

Introduction We started with one frame (B) rotating and accelerating with respect to another(), and obtained the following expression for the absolute acceleration