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

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 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

动力学基本方程式 表示过电位n(或极化电位E和电极反应速 度i间的关系式

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

NEWTONs L丹WS ① BoDY CoNTINUES玉 N TTS STATE OF MOT(0N DR REST UNLESS FORCED DI RECTIoNs IMPoRTA

CoRIoLIS ACcELERAT0 EMYSTIF∈p CONSIOER CASE oF CONSTANT ROTA ToN.No AT0 N OF MME⊙AGUA,ANDc°srAT RADIAL VELOCITY ( As sEEN IN THE RomTIwG 仅AAE

12.1 Systems with controllable linearizations A relatively straightforward case of local controllability analysis is defined by systems with controllable linearizations 12.1.1 Controllability of linearized system Let To: 0, THR, uo: 0, T]H Rm be a