16.61 Aerospace Dynamics Spring 2003 General form of the Transformation Consider a system of n particles ,(Number of dOF=_) g, be a set of generalized coordinates be a set of cartesian coordinates relative to an inertial frame Transformation equations are x=f1(qn,q2q3…qn,1) x2=f2(q,92,q3…qn,t) xn=f, ( g, 92,3,.n,t) Each set of coordinates can have equations of constraint(EOC) e Let / number of eoc for the set of x e Then dof=n-m=3-l Recall: Number of generalized coordinates required depends on the system, not the set selected Massachusetts Institute of Technology C How, Deyst 2003( Based on notes by Blair 2002)16.61 Aerospace Dynamics Spring 2003 Massachusetts Institute of Technology © How, Deyst 2003 (Based on notes by Blair 2002) 10 General Form of the Transformation Consider a system of N particles
(Number of DOF = ) Let: qi be a set of generalized coordinates. i x be a set of Cartesian coordinates relative to an inertial frame Transformation equations are: ( ) ( ) ( ) 1 1123 2 2123 123 ,,, , ,,, , ,,, , n n nn n x fqqq qt x f qqq qt x f qqq qt = = = h h m h Each set of coordinates can have equations of constraint (EOC) • Let l = number of EOC for the set of i x • Then DOF = n – m = 3N – l Recall: Number of generalized coordinates required depends on the system, not the set selected