how to numerically solve a coupled ode?
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Hi,
Please help to solve the following ODE or numerically solve it (get theta(t) and phi(t)):
ODE 1 :
thetaDoubleDot = ((36297*cos(theta))/2 + (80*sin(phi)*(- CA*cos(phi - theta)*phiDot^2 + 4*cos(theta)*thetaDot^2 + CA*phiDoubleDot*sin(phi - theta)))/cos(phi - theta))/((320*sin(phi)*sin(theta))/cos(phi - theta) - 1300/3)
ODE 2:
phiDoulbeDot = (sin(phi - theta)*((1300*thetaDoubleDot)/3 + (36297*cos(theta))/2 + (80*sin(phi)*(- CA*sin(phi - theta)*phiDot^2 + 4*sin(theta)*thetaDot^2 + 4*thetaDoubleDot*cos(theta) + 981/100))/sin(phi - theta)))/(80*CA*cos(phi - theta)*sin(phi))
The thing is that they are coupled. As in the first ODE contain phiDoubleDot and the second ODE contain thetaDoubleDot.
Regards,
采纳的回答
Star Strider
2021-11-8
Use the Symbolic Math Toolbox for this.
First, declare all the appropriate variables as functions of time:
syms theta(t) phi(t) CA T Y
Then define the derivatives as:
Dtheta = diff(theta);
D2theta = diff(theta,2);
Dphi = diff(phi);
D2phi = diff(phi,2);
and make the appropriate substitutions in these equations:
thetaDoubleDot = ((36297*cos(theta))/2 + (80*sin(phi)*(- CA*cos(phi - theta)*phiDot^2 + 4*cos(theta)*thetaDot^2 + CA*phiDoubleDot*sin(phi - theta)))/cos(phi - theta))/((320*sin(phi)*sin(theta))/cos(phi - theta) - 1300/3)
phiDoulbeDot = (sin(phi - theta)*((1300*thetaDoubleDot)/3 + (36297*cos(theta))/2 + (80*sin(phi)*(- CA*sin(phi - theta)*phiDot^2 + 4*sin(theta)*thetaDot^2 + 4*thetaDoubleDot*cos(theta) + 981/100))/sin(phi - theta)))/(80*CA*cos(phi - theta)*sin(phi))
so that they are in the form of:
Eqn1 = D2theta == ((36297*cos(theta))/2 + ...
Eqn2 = D2phi == (sin(phi - theta)* ...
[VF,Subs] = odeToVectorField(Eqn1,Eqn2)
odefcn = matlabFucntion(VF, 'Vars',{T,Y,CA})
Then it should be possible to use ‘odefcn’ with ode45 and the others.
I leave the details to you.
.
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