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16.61 Aerospace Dynamics 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

结构刚度不足对飞机最主要的影响在于, 飞机在飞行速度范围内可能会发生气动弹 性现象,这时的刚度判据就是发生气动弹 性现象时的临界速度V,结构刚度必须要 满足条件V>Vm 气动弹性是与飞机上的气动力、惯性力和 结构的弹性力相关的,是由于飞机在飞行 时载荷作用下的变形和弹性引起的

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16.61 Aerospace Dynamics 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

16.61 Aerospace Dynamics Spring 2003 Lagrange's equations Joseph-Louis lagrange 1736-1813 http://www-groups.dcs.st-and.ac.uk/-history/mathematicians/lagranGe.html Born in Italy. later lived in berlin and paris Originally studied to be a lawyer

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16.61 Aerospace Dynamics Spring 2003 Generalized forces revisited Derived Lagrange s equation from d'Alembert's equation ∑m(8x+16y+22)=∑(Fx+F+F。=) Define virtual displacements sx Substitute in and noting the independence of the 8q,, for each

Lecture #4 16.61 Aerospace Dynamics Extension to multiple intermediate frames(two) Copyright 2002 by Jonathan How