Spring 2003 1661AC22 Longitudinal Dynamics For notational simplicity, let X=Fn, Y= Fu, and Z= F aF Longitudinal equations(1-15 )can be rewritten as mi=X+X2- mg cos(0+△X

LECTURE+ 12 RIGID BODY OYNAAICS 工 MPLICAT IONsF GENERAL ROTATIONAL OYWMICS EJLER's EQUATIN of MOTION TORQVE FREE SPECIAL CASES. PRIMARY LESSONS: 30 ROTATONAL MOTION MUCH MORE COMPLEX THAN PLANAR (20) EULER'S E.o.M. PROVIOE STARTING POINT FoR ALL+ OYwAmIcs SOLUTINS To EvlER's EQuATIONS ARE COMPLEX BUT WE CAN OEVE LOP GooO GEOMETRIC VISUALIZATION TOOLS

ATTITUDE MOTION -TORQVE FeEE MANE 0ISCUSSED THE ROTATIONAL MOTION FRDn 1 ERSPECTvE。FE”6o0 FRAME 一NE0T0F1A0 A WAy TO CONNECT THE MOTION To THE INEATIAL FRAME So WE CAN DESCRI BE THE ACTUAL MOTION TYPICALLY DoNE 6y DESC RI BING MOTION oF NEHICLE ABoVT THE

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

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

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

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

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

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