16.61 Aerospace Dynamics Spring 2003 Generalized Forces Since we have defined generalized coordinates, we need generalized forces to work in the same"space Consider the 2 particle problem X, X X X 1:2. Coordinates: Xi,x2,x3,x4 Constraint: (Gx3)+(x2-x4)=l DOF 4-1=3 Select n-3 generalized coordinates x1+x3 (x,+x q2 tan x3-x1 Can also write the inverse mapping 41,q2,q3,…q Massachusetts Institute of Technology C How, Deyst 2003 (Based on Notes by Blair 2002)16.61 Aerospace Dynamics Spring 2003 Generalized Forces Since we have defined generalized coordinates, we need generalized forces to work in the same ìspace.î Consider the 2 particle problem: (x1, x2) (x3, x4) xi xj l θ (x1, x2) (x3, x4) xi xj l θ ( ) ( ) 1 234 2 2 2 1 3 2 4 Coordinates: , , , Constraint: DOF: 4 1 3 x x x x x x − + − x x = l − = • Select n=3 generalized coordinates: q x x q x x q x x x x 1 1 3 2 2 4 3 1 4 2 3 1 2 2 = + = + = − − − ( ) ( ) tan ( ) ( ) • Can also write the inverse mapping: x f i i = (q1 2 , , q q3,…qn , t) Massachusetts Institute of Technology © How, Deyst 2003 (Based on Notes by Blair 2002) 9