How to solve ODE (vector of first order equations)?

Hello fellow community

I want to solve an ODE for particle trajectory;

function dpos = Throw(pos)  

mu = 1;
g = 10;
dpos(1) = pos(3);
dpos(2) = pos(4);
dpos(3) = -mu * pos(3)* sqrt(pos(3)^2 + pos(4)^2);
dpos(4) = -g - mu * pos(4) * sqrt(pos(3)^2 + pos(4)^2);

end

and there is a problem i encountered right in the beginning:

ode45(@Throw,[0 2],[0 1 1 1])

Error using Throw

Too many input arguments.

Error in odearguments (line 90)

f0 = feval(ode,t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 115)

odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Your help will be apreciated.

Jan

Answer 1

[Star Strider]

The numerical ODE solvers pass a time scalar and a vector to the ODE functions they integrate, in that order, so the function must account for them. Also, by default, MATLAB will create a row vector for the ‘dpos’ elements, so it is necessary to define them as a column vector, since the ODE solvers require that.

This version runs without error:

function dpos = Throw(t,pos)  
mu = 1;
g = 10;
dpos = zeros(4,1);
dpos(1) = pos(3);
dpos(2) = pos(4);
dpos(3) = -mu * pos(3)* sqrt(pos(3)^2 + pos(4)^2);
dpos(4) = -g - mu * pos(4) * sqrt(pos(3)^2 + pos(4)^2);
end

[t,pos] = ode45(@Throw,[0 2],[0 1 1 1]);

figure
plot(t, pos)
grid

.

[JV]

It works. Thanks a lot!

[Star Strider]

As always, my pleasure!