The Lagrange brackets, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\left [{c_j},{c_k}\right ]$$ \end{document}, must be evaluated in terms of the orbital elements and a particular coordinate frame so that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\displaystyle \sum \limits _{k=1}^{6}{\left [ {{c}_{j}},{{c}_{k}} \right ]}{{\dot {c}}_{k}}=\mathbf {F}\cdot \frac {\partial \mathbf {r}}{\partial {{c}_{j}}}, \hspace {0.5in} j=1,2,\dots ,6 $$ \end{document} may be solved for the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $${{\dot {c}}_{k}}$$ \end{document} (i.e., to find the differential equations). (See Eq. 3.41.)
Evaluation of the Lagrange Brackets
Space Technology Library
2021-12-07
39 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
NTRS | 1985
|