环境工程是一门运用工程、技术的方法和手段来控制环境污染及改善环境质量的学科

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

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

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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

P CDN STANT Wow TAKE THE MOMENT OF MOMENTUM (ANGULAR MOMENTUM) MUST EXPLICITLY DEFINE A POWT ABOUT WHICH WE TAKE THE MOMENT

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

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Using control authority to transform nonlinear models into linear ones is one of the most commonly used ideas of practical nonlinear control design. Generally, the trick helps one to recognize \simple\nonlinear feedback design tasks