MATLAB: I have a dynamic system. The equation is ddot = (M)\(F – K*d); Where M,K are (4,4) constant matrix and F and d are vector. I want to solve this equation using ODE45.

MATLABodeode45

In my case The force vector F is variable. The values are changing with time. So to solve ode I've used a for loop. To update the solution of ODE45 I need to use something like this 'T(i,:)'. but it's showing an error 'Subscripted assignment dimension mismatch.' How can I solve an ode for variable dc input?

for i = 1:100
p1 = (power.dat)';
F = p1(:,i);
d0 = [333,333,333,333];
tspan = 0:0.1:1;
[t,T(i,:)] = ode45('Heat',tspan,d0);
end

Best Answer

When you use more than two entries in tspan (as you have done here), the second output of ode45 will be length(tspan) by length(d0) -- that is, it will have the integrals of each of the 4 elements, at each of the time steps. If you only need one of those 4 columns, then output to a variable and select the column you need.

Related Solutions

MATLAB: How to solve this coupled ODE problem using ode solvers

If you want to use the odeNN functions you need to rewrite your 2 2nd-order ODEs into 4 1st-order ODEs, something like this:

function dxdydvxdvydt = your_eqs_of_motion(t,xyvxvy,other,parameters)
x = xyvxvy(1);  % If my ode-equations are complicated 
y = xyvxvy(2);  % I prefer to explicitly extract the
vx = xyvxvy(3); % variables into something that's
vy = xyvxvy(4); % easily human-readable
m = other;
Fx = force_functionx(t,x,y,vx,vy,other,parameters); % Adjust inputs as necessary
Fy = force_functiony(t,x,y,vx,vy,other,parameters);
% or possibly preferable:
% [Fx,Fy] = force_function_xny(t,x,y,vx,vy,other,parameters);
dxdydvxdvydt = [vx;vy;Fx/m;Fy/m];
end

Then you can integrate the equations of motion something like this:

m = 12; % you know what to set for this one
x0y0vx0vy0 = [1e-10,5.08e-5,0,0]; % Your initial conditions
t_span = [0,2*pi];                % a time-span of interest
[t_out,xyvxvy] = ode45(@(t,xyvxvy) your_eqs_of_motion(t,xyvxvy,m,[]),t_span,x0y0vx0vy0);

When integrating equations of motion you typically also have to carefully check that the constants of motion we know should be conserved (total energy, angular momentum, etc.) are reasonably conserved - the general ODE-integrating functions are not guaranteed to do this.

HTH

MATLAB: Ode 45 in a loop

You have a couple of problems with your code. Your ode_research does not follow the ordinary form (dydy = ode_f(t,y)) that ode45 expects. Then your use of a string for the first argument is a bit arcane. I would expect something like this would be better:

t = linspace(1,10);
vf(1) = 30 ; %some random constant value
vfx = vf(1); % needed in the function ode_research_x
x(1) = -3;% starting point for x
vp = v_initial; % or whatever you have as initial condition
for i = 1:length(t)-1
    vfx = vf(1); % this vfx is then used by the ode_research_x function
    [tx,vx] = ode45(@(t,vx) ode_research_x(t,vx,vfx), t(i:i+1), vp(1)); % I am not sure but the time step seems like an issue
    x(i+1) =  x(i) + vx(end).*tx;
    vp(1) = vx;
    vf(1) = 30; % some new constant value calculated in the loop (I've shown a random value)
end
%function to define the ode
function dudt = ode_research_x(t,vx,vfx)
% Some initialization of the constants, I assume.
dudt = 18*mu_f*Cd*Rep*(vx - vfx)/(rho_p*d^2*24); % all the variables except vx and vfx are constant values in the same workspace so I haven't shown their values but they are defined 
end

This looks like some attemt to integrate an equation of motion, if that is the case this is not a good way to go about it. In that case you should integrate the second-order ODE (i.e. the two coupled first order-ODEs) and handle the evolution of the force inside the ode_research_x - function.

HTH

Best Answer

Related Solutions

MATLAB: How to solve this coupled ODE problem using ode solvers

MATLAB: Ode 45 in a loop

Related Question