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a02a0f7..cf3aace 100644 --- a/gravitation/pb_2corps_doc.tex +++ b/gravitation/pb_2corps_doc.tex @@ -15,7 +15,7 @@ \begin{document} \maketitle \section{Présentation} - Cette première partie aborde uniquement le problème théorique et l'établissement des relations et formules indispensables à la réalisation des figures avec `PSTricks' et à l'animation avec le package `\textsf{animate}'. Elle pourra donc sembler superflue à tous ceux qui connaissent bien ce problème classique. De très bons livres traitent le \textit{problème des deux corps} de façon très claire comme celui de José-Philippe Pérez dans `\textit{Mécanique}' aux éditions Masson ou de façon très complète(et très claire aussi) comme celui publié par le \textsc{cnes} aux éditions \textsc{cepadues} : `\textit{Le mouvement du satellite}'. + Cette première partie aborde uniquement le problème théorique et l'établissement des relations et formules indispensables à la réalisation des figures avec `PSTricks' et à l'animation avec le package `\textsf{animate}'. Elle pourra donc sembler superflue à tous ceux qui connaissent bien ce problème classique. De très bons livres traitent le \textit{problème des deux corps} de façon très claire comme celui de José-Philippe Pérez dans ``\textit{Mécanique}'' aux éditions Masson ou celui publié par le \textsc{Cnes} aux éditions \textsc{cepadues} : ``\textit{Le mouvement du satellite}'' qui est, comme on s'en doute, très complet. La deuxième partie détaillera la procédure suivie pour réaliser les schémas et les animations. Toutefois, on peut, dès à présent, avoir accès au code des figures dans le fichier source de ce document. \section{Étude théorique} @@ -269,7 +269,7 @@ Pour \uput{1.6}[!theta_0 2 div](0,0){$\theta$}} \end{pspicture} \end{center} -Pour la suite, retenons que dans $\mathcal{R}*$ : +Pour la suite, retenons que dans $\mathcal{R}^*$ : \[ \overrightarrow{u}_r= \left| @@ -661,7 +661,7 @@ On distingue trois cas : \item $\mathrm{e}=1$ ou $\mathcal{E}=0$ : parabole \item - $\mathrm{e}=>$ ou $\mathcal{E}>0$ : hyperbole + $\mathrm{e}>1$ ou $\mathcal{E}>0$ : hyperbole \end{itemize} Et on s'intéresse maintenant au mouvement elliptique. Les conditions initiales $(\overrightarrow{r}_0,\overrightarrow{v}_0)$ doivent vérifier : \[ -- 2.20.1