I have a set of second order differential nonlinear equation and I want to solve them together with ode45, how could I write codes for them?or better to say I want to define state transition function for such equations.

first three equations all variable and constants are not in vector or matrix form but 4th equation is a 3by1 vector like this:

x''=y'+y+x-(x)/(x^2+y^2+z^2)^1.5+1
y''=x'-x+y-y/(x^2+y^2+z^2)^1.5
z''=-z/(x^2+y^2+z^2)^1.5
m''=[x'' y'' z'']'+[1 2 3]

and I want to write function for this system like this function that i have found in one of matlab example:

function dxdt = vdpStateFcnContinuous(x)
%vdpStateFcnContinuous Evaluate the van der Pol ODEs for mu = 1
dxdt = [x(2); (1-x(1)^2)*x(2)-x(1)];
end

[madhan ravi]

please upload the latex form of the equation

[roya afshar]

I dont have Latex but I write like this:

syms x(t) y(t) z(t) m(t)
eqn1 = diff(x,t,2) == diff(y,t)+y+x-((x)/(x^2+y^2+z^2)^1.5)+1;
eqn2 = diff(y,t,2) == diff(x,t)-x+y-((y)/(x^2+y^2+z^2)^1.5);
eqn3 = diff(z,t,2) ==-(z)/(x^2+y^2+z^2)^1.5;
eqn4 = diff(m,t,2) == [eqn1 eqn2 eqn3]'+[1;2;3];
latex(eqn1)
latex(eqn2)
latex(eqn3)
latex(eqn4)

is it ok?

Answer 1

[madhan ravi]

I believe :

[t,x]=ode45(@eqns,[0 10],[1;0;0;0;0;0;0;0;0;0;0;0]); % function call
plot(t,x(:,1))  % to plot the solution

function dxdt = eqns(t,x)  % function definition
dxdt = [x(2);
    x(4)+x(5)+x(1)-(x(1)/((x(1)^2+x(3)^2+x(5)^2)^1.5))+1;
    x(4);
    x(2)-x(1)+x(3)-(x(3)/((x(1)^2+x(3)^2+x(5)^2)^1.5));
    x(6);
    -x(5)/((x(1)^2+x(3)^2+x(5)^2)^1.5);
    x(2:2:6);
    [x(4)+x(5)+x(1)-(x(1)/((x(1)^2+x(3)^2+x(5)^2)^1.5))+1;x(2)-x(1)+x(3)-(x(3)/((x(1)^2+x(3)^2+x(5)^2)^1.5));-x(5)/((x(1)^2+x(3)^2+x(5)^2)^1.5)]+[1;2;3]];
end

[roya afshar]

Thank you so much Sir.

[madhan ravi]

Anytime :)

Answer 2

[roya afshar]

function dxdt = eqns(x)
one = 7:9;
two = 10:12;
dxdt = [x(2);
    x(4)+x(5)+x(1)-(x(1)/((x(1)^2+x(3)^2+x(5)^2)^1.5))+1;
    x(4);
    x(2)-x(1)+x(3)-(x(3)/((x(1)^2+x(3)^2+x(5)^2)^1.5));
    x(6);
    -x(5)/((x(1)^2+x(3)^2+x(5)^2)^1.5);
    x(tw0);
    [x(4)+x(5)+x(1)-(x(1)/((x(1)^2+x(3)^2+x(5)^2)^1.5))+1;x(2)-x(1)+x(3)-(x(3)/((x(1)^2+x(3)^2+x(5)^2)^1.5));-x(5)/((x(1)^2+x(3)^2+x(5)^2)^1.5)]+[1;2;3]];
end

Could it be true answer? Could anyone make me sure about the answer please?