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adding ode

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02_lois_de_newton.md
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......@@ -910,8 +910,8 @@ sera plus élevée, plus faible, la même? Que se passe-t-il s'il y a une force
Travail pratique (Calcul de force résultante) #
Générer un tableau contenant $N$ particules représentées par leur masse $m_i$
et leur position $\vec r_i$., sachant que:
Générer un tableau contenant $N$ particules, numérotées $p_i$, représentées par leur masse $m_i$
et leur position $\vec r_i$, sachant que:
* La position des particules est aléatoire dans le domaine $[0, 10]\times[0, 10]\m^2$.
* La masse des particules est aléatoire dans le domaine $[0,10]\kg$.
......@@ -923,10 +923,10 @@ et leur position $\vec r_i$., sachant que:
\end{equation}
où $\vec F_{ij}$ est la force gravitationnelle entre la particule $i$ et la particule $j$, et est donnée par
\begin{equation}
\vec F_{ij}=G\frac{m_i m_j}{||\vec r_{ij}||}\vec r_{ij},
\vec F_{ij}=G\frac{m_i m_j}{||\vec r_{ij}||^2}\vec r_{ij},
\end{equation}
où $\vec r_{ij}$ est le vecteur reliant la particule $i$ à la particule $j$.
2. Si chaque particule a de plus une vitesse $\vec v_i$, calculer la force résultante sur chaque particule si $k=10 \kg/\s$.
2. Si chaque particule, $p_i$, a de plus une vitesse $\vec v_i$, calculer la force résultante sur chaque particule si $k=10 \kg/\s$.
---
......@@ -945,8 +945,16 @@ généraliser un petit pou tout ça, en supposant que la vitesse et l'accéléra
également du temps, $\vec v(t)$ et $\vec a(t)$. Pour les besoins de ce cours, nous allons utiliser des
*approximations* numérique des valeurs de $x(t)$, $v(t)$, et $a(t)$.
Pour simplifier, nous allons *discrétiser* le temps. Au lieu de laisser le temps prendre n'importe quelle
valeur réelle positive, $t\in\real^+$, il ne pourra prendre que les valeurs suivantes:
\begin{equation}
t_j=j\cdot \delta t,
\end{equation}
$\delta t>0$ étant le pas de discrétisation temporel et $j\in\integer^+$.
### Le mouvement sans accélération
Supposons
Supposons que pour notre particule $P$, nous connaissons sa position initiale, $\vec x(0)$ et sa vitesse
en tout temps, $\vec v(t)$. Nous souhaitons connaître une approximation de la position $\vec x(t_j)$
figs/time_discr.svg 0 → 100644
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