NUMERICAL SOLUTION GIEN A COMPLEX SET of OYNAMICS (t)=F(x) WHERE F() COULD BE A NONLINEAR FUNCTION IT CAN BE IMPOSS IBLE To ACTVALLY SOLVE FoR ( ExACTLY. OEVELOP A NUMERICAL SOLUTION. CANNED CoDES HELP US THIS TN MATLAB BUT LET US CONSDER THE BASiCS

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 Interest in math from reading halleys 1693 work on

FURTHER BASICS 5-1 · LINEAR MOMENTUM m NEWTON'S LAW ∴F=P ow TAKE THE MOMENT OF MDMENTUM ANGULAR MOMENTUM MUST EXPLICITLY OEFINE

EROSPACE DYNAMiCS EXAMPLE: GWE ACCELERATIoN of THE TIP 0F认ERU0毛R人TM5Hc人AF LDk小 G For A650LUT # CCELER升T10 N UTH RES/∈ct T0wE工NERT1 AL FRAME (∈ TH IN THiS CASE)

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 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