Solve system of differential equations
4 views (last 30 days)
Show older comments
I am facing problem in solving the differential equation
is a vector () as shown in code and is also a vector (). x11=[x1,y1]. I want to solve , where represents derivative with respect to time. Can any one help me to find out x11 vs time. (Note and x11 are the same.) (Preferably use fsolve as I tried using it).
close all
clear all
clc
x01=-5;y01=-7;
x0=[x01,y01]';
beta=25;
syms x1 y1 t
x11=[x1,y1]';
c1=(1/2)*(x1-i*sin(t))^2+(3/2)*(y1-i*cos(t))^2;
row=100*exp(0.1*t);
g1=y1-x1-cos(t);
L1=c1-(1/row)*log(1-row*g1);
grad1 = gradient(L1,x11');
hess1 = hessian(L1,x11');
phi1=-(hess1)^(-1)*(grad1+diff(grad1,t));
u1=-beta*(hess1)^(-1)*x11+phi1
2 Comments
Torsten
on 16 May 2022
u1 is a 2x2 matrix, x11 is a 2x1 vector.
What do you mean by
x11dot = u1
?
Maybe you mean
x11dot = u1*x1
?
Accepted Answer
Torsten
on 16 May 2022
x01=-5;y01=-7;
x0=[x01,y01]';
beta=25;
syms x1 y1 t
x11=[x1,y1]';
c1=(1/2)*(x1-i*sin(t))^2+(3/2)*(y1-i*cos(t))^2;
row=100*exp(0.1*t);
g1=y1-x1-cos(t);
L1=c1-(1/row)*log(1-row*g1);
grad1 = gradient(L1,x11');
hess1 = hessian(L1,x11');
phi1=-(hess1)^(-1)*(grad1+diff(grad1,t));
u1=-beta*(hess1)^(-1)*x11+phi1
fun = matlabFunction(u1,'Vars',{t,x1,y1})
fun = @(t,y)fun(t,x1,y1);
y0 = [x01,y01];
tspan = [0 1]
[T,Y] = ode45(fun,tspan,y0)
plot(T,[real(Y),imag(Y)])
More Answers (0)
See Also
Categories
Find more on Symbolic Math Toolbox in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!