16.61 Aerospace Dynamics Spring 2003 Generalized Coordinates No specific set of coordinates is required to analyze the stem Number of coordinates depends on the system and not the set selected Any set of parameters that are used to represent a system are called generalized coordinates Coordinate Transformation Often find that the "best set of generalized coordinates used to solve a problem may not provide the information needed for further analysis e Use a coordinate transformation to convert between sets of generalized coordinates Example: Work in polar coordinates, then transform to rectangular coordinates, e.g x=rsin 0 cos y=rsin Asin g z=rcos e Massachusetts Institute of Technology C How, Deyst 2003( Based on notes by Blair 200216.61 Aerospace Dynamics Spring 2003 Massachusetts Institute of Technology © How, Deyst 2003 (Based on notes by Blair 2002) 9 Generalized Coordinates • No specific set of coordinates is required to analyze the system. • Number of coordinates depends on the system, and not the set selected. • Any set of parameters that are used to represent a system are called generalized coordinates. Coordinate Transformation • Often find that the “best” set of generalized coordinates used to solve a problem may not provide the information needed for further analysis. • Use a coordinate transformation to convert between sets of generalized coordinates. Example: Work in polar coordinates, then transform to rectangular coordinates, e.g. sin cos sin sin cos x r y r z r θ φ θ φ θ = = =