Sources complètes + doc

Author: flef

Euler.ml

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+(*
+ 	Two-Body-Problem
+    Copyright (C) 2010-2011  Florian Lefèvre
+
+    This program is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Affero General Public License as
+    published by the Free Software Foundation, either version 3 of the
+    License, or (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU Affero General Public License for more details.
+
+    You should have received a copy of the GNU Affero General Public License
+    along with this program.  If not, see <http://www.gnu.org/licenses/>.
+*)
+#open "float";;
+
+(*Création d'une matrice de taille adaptée*)
+let create_vect xo xf dx = make_matrix (int_of_float((xf-xo)/dx + 1./dx + dx)) 2 0.;;
+
+(*Euler 1 - récursive*)
+
+let rec euler1 f' yo xo xf dx =
+	let y1 = yo + f'(xo,yo) * dx in
+	match xo with
+	|xo when xo < xf	-> (xo,yo)::(euler1 f' y1 (xo + dx) xf dx); 
+	|_ 								-> []
+;;
+
+(*Euler 1 - itérative*)
+
+let euler1 f' yo xo xf dx =
+	let i = ref xo and ii = ref 0 
+		and vect = (create_vect xo xf dx) in
+			let y = ref yo in
+					while !i <= xf do
+					(vect.(!ii).(0) <- !i);
+					(vect.(!ii).(1) <- !y);
+					y  := !y + f'(!i,!y) * dx;
+					i := !i + dx;
+					incr ii; 
+				done;
+			vect;;
+
+(*Euler 2*)
+
+let euler2 f'' y'o yo xo xf dx =
+	let y'' = ref (f''(xo,yo,y'o)) and y' = ref y'o and y = ref yo in
+		let i = ref xo and ii = ref 0
+		and vect = (create_vect xo xf dx) in
+			while !i <= xf do
+				(vect.(!ii).(0) <- !i);
+				(vect.(!ii).(1) <- !y);
+				y   := !y + dx * ( !y' + ( !y'' * dx));
+				y'  := !y' + !y'' * dx;
+				y'' := f''(!i,!y,!y');
+				i := !i + dx;
+				incr ii; 
+			done;
+vect;;
+
+(* 	
+	- Version finale (Copie de Méthode d'Euler 8.ml)
+*)
+

Exemples.ml

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+(*
+ 	Two-Body-Problem
+    Copyright (C) 2010-2011  Florian Lefèvre
+
+    This program is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Affero General Public License as
+    published by the Free Software Foundation, either version 3 of the
+    License, or (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU Affero General Public License for more details.
+
+    You should have received a copy of the GNU Affero General Public License
+    along with this program.  If not, see <http://www.gnu.org/licenses/>.
+*)
+
+include "SystemeNonPerturbe.ml";;
+
+(*Exemple 1*)
+(*Deux masses sans vitesse initiale en interaction gravitationnelle*)
+
+let A = {masse = 5e12; rayon = 5; coord_x = 250. ; coord_y = 200.; vitesse_x = 0.; vitesse_y = 0.};;
+let B = {masse = 1e13; rayon = 7; coord_x = 50.; coord_y = 300.; vitesse_x = 0.; vitesse_y = 0.};;
+
+solve A B 0.001;;
+
+(*Exemple 2*)
+(*Cas d'une masse négligeable devant la seconde*)
+
+let A = {masse = 1e17; rayon = 25; coord_x = 300. ; coord_y = 200.; vitesse_x = 0.; vitesse_y = 0.};;
+let B = {masse = 300.; rayon = 3; coord_x = 450.; coord_y = 200.; vitesse_x = 0.; vitesse_y = 200.};;
+
+solve A B 0.0001;;
+
+(*Exemple 3*)
+(*Deux masses égales en interaction*)
+
+let A = {masse = 3e18; rayon = 5; coord_x = 150.; coord_y = 200.; vitesse_x = 0.;  vitesse_y = -500. };;
+let B = {masse = 3e18; rayon = 5; coord_x = 400.; coord_y = 200.; vitesse_x = 0.; vitesse_y = 500.};;
+
+solve A B 0.0001;;
+
+(*Exemple 3 bis*)
+(*Deux masses égales en interaction sur une orbite circulaire*)
+
+let A = {masse = 3e18; rayon = 5; coord_x = 100.; coord_y = 200.; vitesse_x = 0.;  vitesse_y = -500. };;
+let B = {masse = 3e18; rayon = 5; coord_x = 500.; coord_y = 200.; vitesse_x = 0.; vitesse_y = 500.};;
+
+solve A B 0.0001;;
+
+(*Exemple 4*)
+(*Centre de masse en Mouvement Rectiligne Uniforme*)
+
+let A = {masse = 1e17; rayon = 25; coord_x = 0. ; coord_y = 0.; vitesse_x = 25.; vitesse_y = 25.};;
+let B = {masse = 300.; rayon = 3; coord_x = 150.; coord_y = 0.; vitesse_x = 0.; vitesse_y = 250.};;
+
+solve A B 0.0001;;
+
+
+(*Simulation Terre-Lune*)
+(*
+- Données :
+- Masse de la Terre   : ~ 5,9736 x 10 ^ 24 Kg.
+- Masse de la Lune    : ~ 7,3477 x 10 ^ 22 Kg.
+- Distance Terre-Lune : ~ 384 400 Km.
+- Vitesse orbitale de la Lune : 1,022 Km/s.
+- Donnée de vérification de la simulation :
+- Vitesse de libération	: 2,38 km/s
+- Période de révolution	: 27,321582 Jours (Soit ~ 2 360 584 s).
+*)
+
+let Terre = {masse = 5.9736e24; rayon = 6000000; coord_x = 0.;     	 coord_y = 500000.; vitesse_x = 0.;  vitesse_y = 0.};;
+let Lune  = {masse = 7.3477e22; rayon = 1737400; coord_x = 384.4e6;	 coord_y = 500000.; vitesse_x = 0.;  vitesse_y = 1.022e3};;
+
+solve Terre Lune 1.;;
+
+(***************************)
+(*Première vitesse cosmique*)
+
+(*Echec de lancement*)
+
+let Terre = {masse = 5.9736e24; rayon = 6378000; coord_x = 0.;     	 coord_y = 500000.; vitesse_x = 0.;  vitesse_y = 0.};;
+let Sat  = {masse = 1e3; rayon = 1; coord_x = 6378100.;	 coord_y = 500000.; vitesse_x = 0.;  vitesse_y = 7.900e3};;
+
+solve Terre Sat 0.001;;
+
+(*Mise en orbite correct*)
+let Terre = {masse = 5.9736e24; rayon = 6378000; coord_x = 0.;     	 coord_y = 500000.; vitesse_x = 0.;  vitesse_y = 0.};;
+let Sat  = {masse = 1e3; rayon = 1; coord_x = 6378100.;	 coord_y = 500000.; vitesse_x = 0.;  vitesse_y = 7.950e3};;
+
+solve Terre Sat 0.001;;
+
+(*Deuxième vitesse cosmique*)
+
+(*Echec de libération*)
+
+let Terre = {masse = 5.9736e24; rayon = 6378000; coord_x = 0.;     	 coord_y = 500000.; vitesse_x = 0.;  vitesse_y = 0.};;
+let Sat  = {masse = 1e3; rayon = 1; coord_x = 6378100.;	 coord_y = 500000.; vitesse_x = 0.;  vitesse_y = 11.100e3};;
+
+solve Terre Sat 0.001;;
+
+(*Le satellite échappe à l'attraction de la Terre*)
+let Terre = {masse = 5.9736e24; rayon = 6378000; coord_x = 0.;     	 coord_y = 500000.; vitesse_x = 0.;  vitesse_y = 0.};;
+let Sat  = {masse = 1e6; rayon = 1; coord_x = 6378100.;	 coord_y = 500000.; vitesse_x = 0.;  vitesse_y = 11.300e3};;
+
+solve Terre Sat 0.001;;
+
+
+
+