MATLAB: Solve a variable and then the second order differential equation (ODE45)

differential equationsode45second order

Hello,

I have my dynamic equation M*q'' +C*q'+g=Tau and I created a program using ODE45 to solve q and q' as follows:

 qinit=[0;0;0]; % q(0), q'(0) and q''(0)
[t,y] = ode45(@EQM,[0,1],qinit);
 function dqdt = EQM(t,q)
Tau=M*q(3) +C*q(2)+g;
dqdt=[q(2);M^-1(Tau-C*q(2)-g)]

But in ode45 the vector returned by ODE function (EQM) and the initial conditions vector (qinit) must have the same number of elements.

What can I do if I need to solve my EQM having a q'' initial condition?

Thanks in advance!

Best Answer

You can't prescribe q'' since it is automatically given by

q'' = M^(-1)*(tau-g-C*q')

Best wishes

Torsten.

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MATLAB: How to solve first-order nonlinear differential equation where the solution is coupled with an integral

Hi Califfo;

This may be in line with what you want. At least it's changing size It's based on the idea that you know not only qdot, but also lambdadot. That quanity is simply the integrand, .01*q*xdot, and you know that lambda has a starting value of 1. You can make a vector from [q, lambda], which I arbitrarily called z, and then use ode45..

tspan = [0 pi*10];
g0 = 0;
lam0 = 1;
z0 = [g0; lam0];
[t,z] = ode45(@fun, tspan, z0);
x = t.*sin(t);
plot(x,z(:,1))
function zdot = fun(t,z)
  xdot = t*cos(t)+sin(t);
  q =   z(1);
  lam = z(2);
  qdot = xdot*(1-(abs(q))*(lam/2)*(1+ sign(xdot*q)));
  lamdot = 0.01*q*xdot;
  zdot = [qdot; lamdot]
end

MATLAB: How to write Continue Long Statements on Multiple Lines

Use repmat to avoid manually typing all 160 of those ‘%q’ repeats!

Try this:

formatSpec = ['%f',repmat('%q',1,160), '%[^\n\r]'];

Best Answer

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MATLAB: How to write Continue Long Statements on Multiple Lines

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