ode45 returns NAN, HOW could I modify it?

clear
clc
[t,x]=ode45(@eqns,[0.1:0.2:100],[10;0.01;100;-0.0225;10;-0.01]);
for i=1:6
plot(t,x(:,i))
hold on
end
function dxdt = eqns(t,x)  % function definition
m=9.0807;
v1=6;
v2=150;
rc=1;
 
dxdt = [x(2);
    2*v1*x(4)+v2*x(3)+v1^2*x(1)-(m*(rc+x(1)))/(((rc+x(1))^2+(x(3))^2+(x(5))^2)^1.5)+(m/rc^2);
    x(4);
    2*v1*x(2)-v2*x(1)+(v1^2)*x(3)-m*x(3)/(((rc+x(1))^2+x(3)^2+x(5)^2)^1.5);
    x(6);
    (-m*x(5))/(((rc+x(1))^2+x(3)^2+x(5)^2)^1.5);]
end

Answer 1

[madhan ravi]

Reduce the time span and increase time steps (or don't put any time step let matlab assume it) for instance from 0 to 1 -> [0 1] .

Add figure before plot(...) and remove hold on so that each solution can be viewed nicely.

[t,x]=ode45(@eqns,[0 10],[10;0.01;100;-0.0225;10;-0.01]); % change to this
                   % ^^----example
for i=1:6
figure   % add this
plot(t,x(:,i))
% hold on %% remove this
end       

Answer 2

[Star Strider]

After about ‘t=60’, your differential equation saturates (becomes greater than realmax (link)), and subsequent values are NaN. You need to examine your differential equations to be certain that you have coded them correctly, and that the constants are correct.

Take a look at a higher-resolution version of the output of your system:

tspan = linspace(0, 10, 5000);
[t,x]=ode45(@eqns,tspan,[10;0.01;100;-0.0225;10;-0.01]);

semilogy(t,abs(x))

That could give you some idea of where the problems are.

Also see the documentation section on how to Debug a MATLAB Program (link).