<simulation>
<header>
<title>Pendule (avec animation)</title>
<title lang="english">Pendulum (with animation)</title>
<title lang="spanish">Péndulo (con animación)</title>
<author>Stéphane Mottelet, Guillaume Barbaud</author>
<date>Fri Sep 23 16:20:11 CEST 2005</date>
<keywords>simulation,scilab,xml</keywords>
<keywords lang="spanish">Simulación, Scilab, XML</keywords>
</header>
<notes>
<p>Il s'agit d'une simulation d'un pendule non linéaire. On compare la trajectoire obtenue après
intégration des équations à l'aide de Scilab, avec la solution linéarisée. Une fenêtre montre les
deux trajectoires superposées, l'autre permet de visualiser une animation simultanée du pendule "linéaire"
et de son équivalent "non linéaire".
</p>
</notes>
<notes lang="english">
<p>This applet show a simulation of a non-linear pendulum. We compare the trajectory which is obtained by
integrating the equations with Scilab, with the linearized solution. One window allows to see the superposition of
both trajectories and the other one allows to see an animation of the "linear" pendulum and its
"non linear" companion.
</p>
</notes>
<notes lang="spanish">
<p>Se trata aquí de una simulación de un péndulo no lineal. Se compara la trayectoria obtenida después de la integración de las ecuaciones gracias a Scilab, con la solución linearizada. Una ventana enseña las dos trayectorias superpuestas, otra permite visualizar una animación simultanea del péndulo "lineal" y de su equivalente "no lineal"</p>
</notes>
<parameters><section>
<title>Paramètres du pendule</title>
<title lang="english">Parameters of the pendulum</title>
<title lang="spanish">Parámetros del péndulo</title>
<scalar label="L" unit="m"><name>Longueur du pendule</name><name lang="english">Length of the pendulum</name><name lang="spanish">Longitud del péndulo</name><value>1</value></scalar>
<scalar increment="0.001" label="theta_0" max="3.141" min="0.01" unit="rad"><name>Angle initial</name><name lang="english">Initial angle</name><name lang="spanish">Angulo inicial</name><value>0.1</value></scalar>
<scalar label="g0" unit="ms^-2"><name>Accélération de la pesanteur</name><name lang="english">Gravity</name><name lang="spanish">Aceleración de la gravedad</name><value>9.81</value></scalar>
</section><section>
<title>Paramètres de résolution</title>
<title lang="english">Resolution parameters</title>
<title lang="spanish">Parámetros de resolución</title>
<scalar label="tf" unit="s"><name>Temps final</name><name lang="english">Final time</name><name lang="spanish">Tiempo final</name><value>20</value></scalar>
</section><section>
<title>Animation</title>
<title lang="english">Animation</title>
<title lang="spanish">Animación</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="spanish">Instante de visualización</name><value>1</value></scalar>
</section></parameters>
<compute>
<defdomain1d label="tc">
<interval steps="31">
<initialvalue>0</initialvalue>
<finalvalue>2*3.1415926535</finalvalue>
</interval>
</defdomain1d>
<defdomain1d label="t" unit="s">
<name>Temps</name>
<name lang="english">time</name>
<name lang="spanish">Tiempo</name>
<interval steps="500">
<initialvalue>0</initialvalue>
<finalvalue>tf</finalvalue>
</interval>
</defdomain1d>
<ode label="pendule" dependencies="theta_0 tf L g0">
<refdomain1d ref="t" />
<states>
<state label="theta" unit="rad">
<name>Solution Réelle</name>
<name lang="english">Real Solution</name>
<name lang="spanish">Solución real</name>
<derivative>theta_point</derivative>
<initialcondition>theta_0</initialcondition>
</state>
<state label="theta_point" unit="rad">
<name>dérivée de l'angle</name>
<name lang="english">Derivative of angle</name>
<name lang="spanish">Derivada del ángulo</name>
<derivative>-g0/L*sin(theta)</derivative>
<initialcondition>0</initialcondition>
</state>
</states>
<outputs>
<output label="thetalin">
<name>Solution linéarisée</name>
<name lang="english">Linearized solution</name>
<name lang="spanish">Solución linearizada</name>
<value>theta_0*cos(sqrt(g0/L)*t)</value>
</output>
</outputs>
</ode>
</compute>
<graphs>
<parametriccurve2d label="circ1">
<refdomain1d ref="tc" />
<x1>
<value>L*sin(theta(iv))+cos(tc)*L/20</value>
</x1>
<x2>
<value>-L*cos(theta(iv))+sin(tc)*L/20</value>
</x2>
</parametriccurve2d>
<parametriccurve2d label="circ2">
<refdomain1d ref="tc" />
<x1>
<value>2+L*sin(thetalin(iv))+cos(tc)*L/20</value>
</x1>
<x2>
<value>-L*cos(thetalin(iv))+sin(tc)*L/20</value>
</x2>
</parametriccurve2d>
<polyline label="pendule_nonlin">
<vertex x1="0" x2="0" />
<vertex x1="L*sin(theta(iv))" x2="-L*cos(theta(iv))" />
</polyline>
<polyline label="pendule_lin">
<vertex x1="2" x2="0" />
<vertex x1="2+L*sin(thetalin(iv))" x2="-L*cos(thetalin(iv))" />
</polyline>
</graphs>
<display>
<window>
<title>Animation des pendules</title>
<title lang="english">Pendulum's animation</title>
<title lang="spanish">Animación de los péndulos</title>
<axis2d iso="yes" xmax="3" xmin="-1" ymax="1" ymin="-1.5">
<drawcurve2d color="red" ref="pendule_nonlin" />
<drawcurve2d color="red" ref="circ1" />
<drawcurve2d color="blue" ref="pendule_lin" />
<drawcurve2d color="blue" ref="circ2" />
</axis2d>
</window>
<window dependencies="theta_0 tf L g0">
<title>Comparaison des deux solutions</title>
<title lang="english">Comparison of both solutions</title>
<title lang="spanish">Comparación de las soluciones</title>
<axis2d xmax="tf" xmin="0" ymax="theta_0" ymin="-theta_0">
<drawcurve2d color="red" ref="theta" thickness="2" />
<drawcurve2d color="blue" ref="thetalin" thickness="2" />
</axis2d>
</window>
</display>
</simulation>