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## APPENDIX A

## Nomenclature and Notation

### Nomenclature

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• Unit vectors along the *x*, *y*, and *z* axes are denoted as **i**, **j**, and **k**, respectively.

• A coordinate frame is denoted by , and a superscript denotes the label of the frame. For example, is the inertial coordinate frame.

• Given a vector **p** ^{3}, the expression of **p** in the coordinates of frame is denoted as **p**^{a}.

• Given a vector **p** ^{3}, the first, second, and third components of p expressed with respect to the coordinates of are denoted as , , and , respectively.

• A rotation matrix from frame to is denoted as .

• The transpose of a matrix *M* is denoted as *M*^{T}.

• Differentiation of a scalar with respect to time is denoted by a “dot” (e.g., ). Differentiation of a vector with respect to frame is denoted by .