Problème d'équation [Résolu]

[irarref]

Salut à tous,

voici toutes les équations que j'ai, ça ne donne aucun résultat et j'ai tout essayé.

Code :

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AA := cos(theta1)*(cos(theta1)*sin(theta2)*d5+(cos(theta1)*cos(theta2)*cos(theta3)+sin(theta1)*sin(theta3))*d4-cos(theta1)*d2)+sin(theta1)*(sin(theta1)*sin(theta2)*d5+(sin(theta1)*cos(theta2)*cos(theta3)-cos(theta1)*sin(theta3))*d4-sin(theta1)*d2)-100*cos(theta2)*(cos(theta3)*cos(theta4)-sin(theta3)*sin(theta4))-10*cos(theta2)*(-cos(theta3)*sin(theta4)-sin(theta3)*cos(theta4))-10*sin(theta2)-cos(theta2)*cos(theta3)*d4-sin(theta2)*d5+d2


> AA2 := -sin(theta1)*(cos(theta1)*sin(theta2)*d5+(cos(theta1)*cos(theta2)*cos(theta3)+sin(theta1)*sin(theta3))*d4-cos(theta1)*d2)+cos(theta1)*(sin(theta1)*sin(theta2)*d5+(sin(theta1)*cos(theta2)*cos(theta3)-cos(theta1)*sin(theta3))*d4-sin(theta1)*d2)+100*sin(theta3)*cos(theta4)+100*cos(theta3)*sin(theta4)+10*cos(theta3)*cos(theta4)-10*sin(theta3)*sin(theta4)+sin(theta3)*d4;



> AA3 := -100*sin(theta2)*(cos(theta3)*cos(theta4)-sin(theta3)*sin(theta4))-10*sin(theta2)*(-cos(theta3)*sin(theta4)-sin(theta3)*cos(theta4))+10*cos(theta2);




> BB := cos(theta1)*cos(theta2)*(cos(theta1)*sin(theta2)*d5+(cos(theta1)*cos(theta2)*cos(theta3)+sin(theta1)*sin(theta3))*d4-cos(theta1)*d2)+sin(theta1)*cos(theta2)*(sin(theta1)*sin(theta2)*d5+(sin(theta1)*cos(theta2)*cos(theta3)-cos(theta1)*sin(theta3))*d4-sin(theta1)*d2)+sin(theta2)*(-cos(theta2)*d5+sin(theta2)*cos(theta3)*d4)+d2*cos(theta2)-100*cos(theta3)*cos(theta4)+100*sin(theta3)*sin(theta4)+10*cos(theta3)*sin(theta4)+10*sin(theta3)*cos(theta4)-cos(theta3)*d4;



> BB2 := -cos(theta1)*sin(theta2)*(cos(theta1)*sin(theta2)*d5+(cos(theta1)*cos(theta2)*cos(theta3)+sin(theta1)*sin(theta3))*d4-cos(theta1)*d2)-sin(theta1)*sin(theta2)*(sin(theta1)*sin(theta2)*d5+(sin(theta1)*cos(theta2)*cos(theta3)-cos(theta1)*sin(theta3))*d4-sin(theta1)*d2)+cos(theta2)*(-cos(theta2)*d5+sin(theta2)*cos(theta3)*d4)-d2*sin(theta2)+10+d5;




> BB3 := sin(theta1)*(cos(theta1)*sin(theta2)*d5+(cos(theta1)*cos(theta2)*cos(theta3)+sin(theta1)*sin(theta3))*d4-cos(theta1)*d2)-cos(theta1)*(sin(theta1)*sin(theta2)*d5+(sin(theta1)*cos(theta2)*cos(theta3)-cos(theta1)*sin(theta3))*d4-sin(theta1)*d2)-100*cos(theta3)*sin(theta4)-100*sin(theta3)*cos(theta4)-10*cos(theta3)*cos(theta4)+10*sin(theta3)*sin(theta4)-sin(theta3)*d4;




> CC := (cos(theta1)*cos(theta2)*cos(theta3)-sin(theta1)*sin(theta3))*(cos(theta1)*sin(theta2)*d5+(cos(theta1)*cos(theta2)*cos(theta3)+sin(theta1)*sin(theta3))*d4-cos(theta1)*d2)+(sin(theta1)*cos(theta2)*cos(theta3)+cos(theta1)*sin(theta3))*(sin(theta1)*sin(theta2)*d5+(sin(theta1)*cos(theta2)*cos(theta3)-cos(theta1)*sin(theta3))*d4-sin(theta1)*d2)+sin(theta2)*cos(theta3)*(-cos(theta2)*d5+sin(theta2)*cos(theta3)*d4)+cos(theta3)*d2*cos(theta2)-100*cos(theta4)+10*sin(theta4)-d4;





> CC2 := (-cos(theta1)*cos(theta2)*sin(theta3)-sin(theta1)*cos(theta3))*(cos(theta1)*sin(theta2)*d5+(cos(theta1)*cos(theta2)*cos(theta3)+sin(theta1)*sin(theta3))*d4-cos(theta1)*d2)+(-sin(theta1)*cos(theta2)*sin(theta3)+cos(theta1)*cos(theta3))*(sin(theta1)*sin(theta2)*d5+(sin(theta1)*cos(theta2)*cos(theta3)-cos(theta1)*sin(theta3))*d4-sin(theta1)*d2)-sin(theta2)*sin(theta3)*(-cos(theta2)*d5+sin(theta2)*cos(theta3)*d4)-sin(theta3)*d2*cos(theta2)-100*sin(theta4)-10*cos(theta4);




> CC3 := -cos(theta1)*sin(theta2)*(cos(theta1)*sin(theta2)*d5+(cos(theta1)*cos(theta2)*cos(theta3)+sin(theta1)*sin(theta3))*d4-cos(theta1)*d2)-sin(theta1)*sin(theta2)*(sin(theta1)*sin(theta2)*d5+(sin(theta1)*cos(theta2)*cos(theta3)-cos(theta1)*sin(theta3))*d4-sin(theta1)*d2)+cos(theta2)*(-cos(theta2)*d5+sin(theta2)*cos(theta3)*d4)-d2*sin(theta2)-10-d5;





> DD := (cos(theta4)*(cos(theta1)*cos(theta2)*cos(theta3)-sin(theta1)*sin(theta3))+sin(theta4)*(-cos(theta1)*cos(theta2)*sin(theta3)-sin(theta1)*cos(theta3)))*(cos(theta1)*sin(theta2)*d5+(cos(theta1)*cos(theta2)*cos(theta3)+sin(theta1)*sin(theta3))*d4-cos(theta1)*d2)+(cos(theta4)*(sin(theta1)*cos(theta2)*cos(theta3)+cos(theta1)*sin(theta3))+sin(theta4)*(-sin(theta1)*cos(theta2)*sin(theta3)+cos(theta1)*cos(theta3)))*(sin(theta1)*sin(theta2)*d5+(sin(theta1)*cos(theta2)*cos(theta3)-cos(theta1)*sin(theta3))*d4-sin(theta1)*d2)+(sin(theta2)*cos(theta3)*cos(theta4)-sin(theta2)*sin(theta3)*sin(theta4))*(-cos(theta2)*d5+sin(theta2)*cos(theta3)*d4)+cos(theta4)*cos(theta3)*d2*cos(theta2)-sin(theta4)*sin(theta3)*d2*cos(theta2)-100;






> DD2 := (-sin(theta4)*(cos(theta1)*cos(theta2)*cos(theta3)-sin(theta1)*sin(theta3))+cos(theta4)*(-cos(theta1)*cos(theta2)*sin(theta3)-sin(theta1)*cos(theta3)))*(cos(theta1)*sin(theta2)*d5+(cos(theta1)*cos(theta2)*cos(theta3)+sin(theta1)*sin(theta3))*d4-cos(theta1)*d2)+(-sin(theta4)*(sin(theta1)*cos(theta2)*cos(theta3)+cos(theta1)*sin(theta3))+cos(theta4)*(-sin(theta1)*cos(theta2)*sin(theta3)+cos(theta1)*cos(theta3)))*(sin(theta1)*sin(theta2)*d5+(sin(theta1)*cos(theta2)*cos(theta3)-cos(theta1)*sin(theta3))*d4-sin(theta1)*d2)+(-sin(theta2)*cos(theta3)*sin(theta4)-sin(theta2)*sin(theta3)*cos(theta4))*(-cos(theta2)*d5+sin(theta2)*cos(theta3)*d4)-sin(theta4)*cos(theta3)*d2*cos(theta2)-cos(theta4)*sin(theta3)*d2*cos(theta2)-10;





> DD3 := -cos(theta1)*sin(theta2)*(cos(theta1)*sin(theta2)*d5+(cos(theta1)*cos(theta2)*cos(theta3)+sin(theta1)*sin(theta3))*d4-cos(theta1)*d2)-sin(theta1)*sin(theta2)*(sin(theta1)*sin(theta2)*d5+(sin(theta1)*cos(theta2)*cos(theta3)-cos(theta1)*sin(theta3))*d4-sin(theta1)*d2)+cos(theta2)*(-cos(theta2)*d5+sin(theta2)*cos(theta3)*d4)-d2*sin(theta2)-10-d5;

Et pour essayer de résoudre ça j'ai utilisé la commande suivante :

Code :

> solve({AA, AA2, AA3, BB, BB2, BB3, CC, CC2, CC3, DD, DD2, DD3}, {theta1, theta2, theta3, theta4});

Je tiens a preciser que je suis passé au '' Maple 15. ''

Merci pour votre aide d'avance

[quentinh]

Si j'ai bien l'oeil, c'est pas des équations mais des expressions, faudrait peut-être que tu dises à Maple à quoi tes expressions doivent être égales.
Au passage, cela m'étonnerais que la commande simplify ne rende pas ces expressions un peu plus... « lisables » peut être ?

[irarref]

j'ai utilisé '' simplify "" et j'ai peut avoir les theta 2,3,4 sans theta1 qui je doit faire varier manuellement.

maintenant mon probleme c'est que j'ai pas une valeur numerique malgré que j'ai donner a chaque variable sauf les theta i biensur une valeur fix.

y'a une instruction pour ca ????

[quentinh]

evalf(variable) résout-il ton problème ?

[irarref]

non pas vraiment

j'ai eu le resultat suivant :

{theta4 = arctan(-1/20+(1/10)*sin(theta3)^2+(1/10)*sqrt(399*sin(theta3)^2-399*sin(theta3)^4), -1/(40*cos(theta3)*sin(theta3))+(1/40)*(-20+40*sin(theta3)^2)*(-1/20+(1/10)*sin(theta3)^2+(1/10)*sqrt(399*sin(theta3)^2-399*sin(theta3)^4))/(cos(theta3)*sin(theta3)))}, {theta4 = arctan(-1/20+(1/10)*sin(theta3)^2-(1/10)*sqrt(399*sin(theta3)^2-399*sin(theta3)^4), -1/(40*cos(theta3)*sin(theta3))+(1/40)*(-20+40*sin(theta3)^2)*(-1/20+(1/10)*sin(theta3)^2-(1/10)*sqrt(399*sin(theta3)^2-399*sin(theta3)^4))/(cos(theta3)*sin(theta3)))}




{theta3 = arctan((1/2)*(10*sin(theta4)+cos(theta4))*sqrt(200+10*sqrt(399-99*sin(theta4)^2-20*sin(theta4)*cos(theta4)))*(-2+(1/10)*sqrt(399-99*sin(theta4)^2-20*sin(theta4)*cos(theta4)))/(99*sin(theta4)^2+20*sin(theta4)*cos(theta4)+1), (1/20)*sqrt(200+10*sqrt(399-99*sin(theta4)^2-20*sin(theta4)*cos(theta4))))}, {theta3 = arctan(-(1/2)*(10*sin(theta4)+cos(theta4))*sqrt(200+10*sqrt(399-99*sin(theta4)^2-20*sin(theta4)*cos(theta4)))*(-2+(1/10)*sqrt(399-99*sin(theta4)^2-20*sin(theta4)*cos(theta4)))/(99*sin(theta4)^2+20*sin(theta4)*cos(theta4)+1), -(1/20)*sqrt(200+10*sqrt(399-99*sin(theta4)^2-20*sin(theta4)*cos(theta4))))}, {theta3 = arctan((1/2)*(10*sin(theta4)+cos(theta4))*sqrt(200-10*sqrt(399-99*sin(theta4)^2-20*sin(theta4)*cos(theta4)))*(-2-(1/10)*sqrt(399-99*sin(theta4)^2-20*sin(theta4)*cos(theta4)))/(99*sin(theta4)^2+20*sin(theta4)*cos(theta4)+1), (1/20)*sqrt(200-10*sqrt(399-99*sin(theta4)^2-20*sin(theta4)*cos(theta4))))}, {theta3 = arctan(-(1/2)*(10*sin(theta4)+cos(theta4))*sqrt(200-10*sqrt(399-99*sin(theta4)^2-20*sin(theta4)*cos(theta4)))*(-2-(1/10)*sqrt(399-99*sin(theta4)^2-20*sin(theta4)*cos(theta4)))/(99*sin(theta4)^2+20*sin(theta4)*cos(theta4)+1), -(1/20)*sqrt(200-10*sqrt(399-99*sin(theta4)^2-20*sin(theta4)*cos(theta4))))}








{theta2 = -arctan(10 cos(theta3) cos(theta4)

- 10 sin(theta3) sin(theta4) - cos(theta3) sin(theta4)

- sin(theta3) cos(theta4))}
>

mais quand je fais : evalf(theta2) ca donne theta2.

[quentinh]

Tu as encore un système d'équations, mais il y a plusieurs solutions à chacun de tes thêta, tu dois pouvoir utiliser fsolve() pour terminer, mais je suis pas sûr… il faut peut-être que tu sélectionne une des solutions pour chaque thêta…

[irarref]

merci pour ton aide quentinh

je pense que je suis dans la bonne voie cette fois.