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APPENDIX A Nomenclature and Notation Nomenclature · Unit vectors along the x, y, and z axes are denoted as i, j, and k, respectively. A coordinate frame is denoted by F, and a superscript denotes the label of the frame. For example, F i is the inertial coordinate frame. · · Given a vector p R 3 , the expression of p in the coordinates of frame F a is denoted as p a . Given a vector p R 3 , the first, second, and third components of p expressed with respect to the coordinates of F a are denoted a a as p x , p a , and p z , respectively. y b A rotation matrix from frame F a to F b is denoted as R a . · · · · The transpose of a matrix M is denoted as M . Differentiation of a scalar with respect to time is denoted by a . "dot" (e.g., x). Differentiation of a vector with respect to frame d F a is denoted by dt a .