<simulation>
<header>
<title lang="french">Système Terre-Lune</title>
<title lang="english">Earth-Moon system</title>
<title lang="german">Erde-Mond-System</title>
<title lang="spanish">Sistema Tierra-Luna</title>
<author>Stéphane Mottelet, Guillaume Barbaud</author>
<date>Fri Sep 23 16:00:41 CEST 2005</date>
<keywords>simulation,scilab,xml</keywords>
<keywords lang="english">simulation,scilab,xml</keywords>
<keywords lang="german">Simulation,Scilab,Xml</keywords>
<keywords lang="spanish">Simulación, Scilab, XML</keywords>
</header>
<notes>
<p>Cette appliquette permet de simuler les trajectoires respectives de la Terre et de la
Lune, avec la possibilité de modifier les masses des deux corps, ainsi que la vitesse
initiale de la Lune. Cela permet de faire apparaîtres des ellipses d'exentricités
variées.</p>
<p>Le fichier source XML est aussi intéressant à visualiser car il montre un exemple
d'utilisation d'états vectoriels dans un élément de type <ode>.
</p>
</notes>
<notes lang="english">
<p>This applet aims to show the respective trajectories of the Moon and the Earth,
with the possibility to change default masses of both, and to change the initial velocity
of the moon.</p>
<p>The source XML is also interesting, as it shows how to use vector states in
an <ode> element.
</p>
</notes>
<notes lang="german">
<p>Diese Anwendung erlaubt eine Simulation der Wegstrecken der Erde und des Mondes, mit der Möglichkeit die Massen der beiden Körper zu modifizieren, sowie die Anfangsgeschwindigkeit des Mondes. Dies erlaubt, verschieden exzentrisierte Ellipsen darzustellen.</p>
</notes>
<notes lang="spanish">
<p>Este programa permite simular las trayectorias respectivas de la Tierra y de la Luna con la posibilidad de modificar las masas de cada uno y la velocidad inicial de la Luna también. Esto permite hacer aparecer elipses con varias excentricidades.</p>
<p> Es también interesante visualizar el fichero fuente XML porque contiene un ejemplo de uso de estados vectoriales en un elemento de tipo <ode>. </p>
</notes>
<parameters><section>
<title>Masses et vitesses initiales</title>
<title lang="english">Masses and initial velocities</title>
<title lang="german">Anfangsmassen und -geschwindigkeiten</title>
<title lang="spanish">Masas y velocidades iníciales</title>
<scalar label="vL0" unit="m"><name>Vitesse de la Lune à l'origine</name><name lang="english">Velocity of the moon at initial time</name><name lang="german">Anfangsgeschwindigkeit des Mondes</name><name lang="spanish">Velocidad de la Luna al inicio</name><value>2*%pi/(27.55*24*3600)*3.84402e8</value></scalar>
<scalar label="mT" unit="m" min="4" max="5.975" increment="0.0001"><name>Masse de la Terre (1e24)</name><name lang="english">Mass of the Earth (1e24)</name><name lang="german">Erdmasse (1e24)</name><name lang="spanish">Masa de la Tierra (1e24)</name><value>5.975</value></scalar>
<scalar label="mL" unit="m" min="0.0735" max="5.975" increment="0.0001"><name>Masse de la Lune (1e24)</name><name lang="english">Masse of the Moon (1e24)</name><name lang="german">Mondmasse (1e24)</name><name lang="spanish">Masa de la Luna (1e24)</name><value>0.0735</value></scalar>
<scalar label="theta" unit="m" min="1" max="179" increment="1"><name>Angle d'attaque de la Lune (degrés)</name><name lang="english">Angle of attack for the Moon (degrees)</name><name lang="german">Angriffswinkel des Mondes</name><name lang="spanish">Angulo de ataque de la Luna (grados)</name><value>90</value></scalar>
</section><section>
<title>Paramètres de résolution</title>
<title lang="english">Resolution parameters</title>
<title lang="german">Lösungsparameter</title>
<title lang="spanish">Parámetros de resolución</title>
<scalar label="jf" unit="s"><name>Temps final (jours)</name><name lang="english">Final time (days)</name><name lang="german">Endzeit (Tage)</name><name lang="spanish">Tiempo final (dias)</name><value>1</value></scalar>
</section><section>
<title>Animation</title>
<title lang="english">Animation</title>
<title lang="german">Animation</title>
<title lang="spanish">Animacion</title>
<scalar label="iv" min="1" max="100" increment="1" period="40"><name lang="english">Visualisation time</name><name>Instant de visualisation</name><name lang="german">Visualisierungsmoment</name><name lang="spanish">Instante de visualización</name><value>1</value></scalar>
</section></parameters>
<compute>
<defdomain1d label="t" unit="s">
<name>Temps</name>
<name lang="english">Time</name>
<name lang="german">Zeit</name>
<name lang="spanish">Tiempo</name>
<interval steps="100">
<initialvalue>0</initialvalue>
<finalvalue>27.55*jf*24*3600</finalvalue>
</interval>
</defdomain1d>
<ode label="terre_lune" dependencies="jf theta mL mT vL0">
<refdomain1d ref="t" />
<states>
<variable label="r3">norm(xT-xL)^3</variable>
<state label="xT" size="2" unit="rad">
<name>Position de la Terre</name>
<name lang="english">Earth's position</name>
<name lang="german">Position der Erde</name>
<name lang="spanish">Posición de la Tierra</name>
<derivative>vT</derivative>
<initialcondition>[0;0]</initialcondition>
</state>
<state label="vT" size="2" unit="rad">
<name>Vitesse de la Terre</name>
<name lang="english">Earth's Velocity</name>
<name lang="german">Geschwindigkeit des Mondes</name>
<name lang="spanish">Velocidad de la Tierra</name>
<derivative>6.67e-11*mL*1e24*(xL-xT)/r3</derivative>
<initialcondition>[0;0]</initialcondition>
</state>
<state label="xL" size="2" unit="rad">
<name>Position de la Lune</name>
<name lang="english">Moon's position</name>
<name lang="german">Position des Mondes</name>
<name lang="spanish">Posición de la Luna</name>
<derivative>vL</derivative>
<initialcondition>[3.84402e8;0]</initialcondition>
</state>
<state label="vL" size="2" unit="rad">
<name>Vitesse de la Lune</name>
<name lang="english">Moons's Velocity</name>
<name lang="german">Geschwindigkeit des Mondes</name>
<name lang="spanish">Velocidad de la Luna</name>
<derivative>6.67e-11*mT*1e24*(xT-xL)/r3</derivative>
<initialcondition>vL0*[cos(%pi*theta/180);sin(%pi*theta/180)]</initialcondition>
</state>
</states>
<outputs>
<output label="xG">
<name>Centre de gravité</name>
<name lang="english">Mass center</name>
<name lang="german">Gravitationszentrum</name>
<name lang="spanish">Centro de Gravedad</name>
<value>(xL*mL+xT*mT)/(mL+mT)</value>
</output>
</outputs>
</ode>
</compute>
<graphs>
<parametriccurve2d label="traj_terre">
<name>Terre</name>
<name lang="english">Earth</name>
<name lang="german">Erde</name>
<name lang="spanish">Tierra</name>
<refdomain1d ref="t" />
<x1>
<value>xT(:,1)-xG(:,1)</value>
</x1>
<x2>
<value>xT(:,2)-xG(:,2)</value>
</x2>
</parametriccurve2d>
<parametriccurve2d label="traj_lune">
<name>Lune</name>
<name lang="english">Moon</name>
<name lang="german">Mondname</name>
<name lang="spanish">Luna</name>
<refdomain1d ref="t" />
<x1>
<value>xL(:,1)-xG(:,1)</value>
</x1>
<x2>
<value>xL(:,2)-xG(:,2)</value>
</x2>
<polyline label="segment">
<vertex x1="xL(iv,1)-xG(iv,1)" x2="xL(iv,2)-xG(iv,2)">
<name>L</name>
<name lang="english">M</name>
<name lang="german">M</name>
<name lang="spanish">L</name>
</vertex>
<vertex x1="xT(iv,1)-xG(iv,1)" x2="xT(iv,2)-xG(iv,2)">
<name>T</name>
<name lang="english">E</name>
<name lang="german">E</name>
<name lang="spanish">T</name>
</vertex>
</polyline>
</parametriccurve2d>
</graphs>
<display>
<window>
<title>Orbites du système</title>
<title lang="english">Orbits of the system</title>
<title lang="german">Umlaufbahnen des Systems</title>
<title lang="spanish">Orbites del sistema</title>
<axis2d position="origin" iso="yes" xmin="-5e8" ymin="-5e8" xmax="5e8" ymax="5e8">
<drawcurve2d ref="traj_lune" />
<drawcurve2d ref="traj_terre" />
<drawcurve2d ref="segment" marker="circle" />
</axis2d>
</window>
</display>
</simulation>