Solve differential equation Systems with ODE45

I want to solve a differental equation system with ODE45.

close all;clc;
%basic planet/moon Parametres%
re=6378e3;
g0=9.81;
rho0=1.225; 
sh=7500; 
%parametres related to the vehicle%
m0=68e3;
Cdrag=0.5;
diameter=5;
area= pi*((diameter/2)^2);
Adrag= area*Cdrag;
Isp=390;
thrust= 933910;
R=15;
%initial calculations%
ceff= Isp*g0;
propflow= thrust/ceff;
mf=m0/R;
mp= m0-mf;
tburn=mp/propflow;
%Functions%
syms h;
rhoh=rho0*exp(-h/sh);
gh=g0*((re/re+h)^2);
r(h)=re+h;

%Pitchover altitude mass and velocity%
syms x
y0=89.85;
hpo=-(g0/2)*(((m0-x)/propflow)^2)+(ceff/propflow)*(x*log(x/m0)+m0-x)==130;
mpo=vpasolve(hpo,x);
vpo=-g0*((m0-mpo)/propflow)-ceff*log(mpo/m0);
tpo=(m0-mpo)/propflow;

%inital conditions%
tRange=[0 tburn];
Y0=[y0;vpo;hpo;0;mpo];
%Solve ODE§
[tSol,YSol]=ode45(@AscentProblem,tRange,Y0);

%Define Functions%
function dYdt= AscentProblem(t,Y)
y=Y(1);
v=Y(2);
h=Y(3);
x=Y(4);
m=Y(5);

dydt=((v(t)/(re+h(t)))-(g0/v(t)).*((re/re+h(t)).^2)).*cos(y(t));
dvdt=(propflow*ceff/m(t))-(Adrag* rhoh.*(v(t).^2))/2*m(t)- gh .*sin(y(t));
dhdt=v(t).*sin(y(t));
dxdt=(re/(re+h(t))).*v(t).*cos(y(t));
dmdt=-propflow;

%Define dYdt%
dYdt=[dydt;dvdt;dhdt;dxdt;dmdt];
end

Array indices must be positive integers or logical values.

Error in sym/subsref (line 870) R_tilde = builtin('subsref',L_tilde,Idx);

Error in APode45>AscentProblem (line 50) dydt=((v(t)/(re+h(t)))-(g0/v(t)).*((re/re+h(t)).^2)).*cos(y(t));

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);

Error in APode45 (line 40) [tSol,YSol]=ode45(@AscentProblem,tRange,Y0);

PLease help, I cannot find my mistake.

[madhan ravi]

learn indexing

Answer 1

[Torsten]

Y0=[y0;vpo;hpo;0;mpo];

must be a vector of doubles.

Check the type of every entry of this vector and modify your code accordingly.

[Brendan Görres]

I changed Y0 to a vector of doubles, but still receive the same errors.

[Torsten]

Replace v(t), h(t) y(t) and m(t) by v,h,y and m.

Further make all the constants you use in AscentProblem accessible there (g0, re, propflow,...)

[Brendan Görres]

Now MatLab gives me these errors.

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);

Error in APode45 (line 43) [tSol,YSol]=ode45(@AscentProblem,tRange,Y0);

Answer 2

[Steven Lord]

The variables you define inside your ODE function as each containing one element of the Y input with which ode45 calls your ODE function (y, v, h, x, and m) are scalars. You shouldn't be trying to index into them using the variable t. t is unlikely to be the exact value 1, meaning it is unlikely to be a valid index into a scalar. Just use y, v, h, x, and m.

[Brendan Görres]

Yes, thank you! It runs now:)