how to solve 3dof point mass equations of motion of flight vehicle

i have to solve 6 differential equations of 3dof system of flight vehicle abd plot them. i have run a code but i am not getting appropriate results.

plzz anyone help me how to do that.

clear all;close all;clc;

t = 0:0.1:15;

y0= [0.5 0.5 0.5 0.5 0.5 0.5];

[tsol ysol] = ode45(@threedof, t, y0);

velocity = ysol(:,1);

yaw_angle = ysol(:,2);

pitch_angle = ysol(:,3);

x = ysol(:,4);

y = ysol(:,5);

z = ysol(:,6);

figure();

plot(tsol,velocity,'or',tsol,yaw_angle,'--k',tsol,pitch_angle,'--b',tsol,x,'oy',tsol,y,'ok',tsol,z,'og')

function solveode = threedof(t,y);

T = 2000; m = 200; g = 9.81; gamma = 10*pi/180; V=100; phi = (10*pi/180); %Vvec= [V;0;0];

D = 00; S=00; L = 0000;

fval(1)=((T/m)-(D/m)-(g*sin(gamma)));

fval(2)=((L/m*V)-(g*cos(gamma)/V));

favl(3)=(S/(m*V*cos(gamma)));

fval(4)=V*cos(gamma)*cos(phi);

fval(5)=V*cos(gamma)*sin(phi);

fval(6)=V*sin(gamma);

solveode = [fval(1);fval(2);favl(3);fval(4);fval(5);fval(6)];

end

[Sam Chak]

Hi Flight engineer,

What are the expected appropriate results?

Notice that your pitch angle is flying at 0.5 rad, where 1 rad is approx 57.3°. The aircraft is not going to stall?

Answer 1

[Bjorn Gustavsson]

A three-degrees-of-freedom dynamic system in three spatial coordinates doesn't have yaw and pitch degrees of freedom. It is effectively modeling the trajectory of a particle. As such your ODE-function looks dodgy. My standard way of writing equations-of-motion are, something like:

function d2ydt2dydt = threedof(t,y) 
T = 2000; % describe units...
m = 200;
g = 9.81;
gamma = 10*pi/180; 
phi = (10*pi/180); %Vvec= [V;0;0];
D = 0; % Drag?
S = 0; % Some other parameter?
L = 0; % Lift

V = y(1:3); % I prefer to order the state-vector as [r;v], but this is purely convention 
T = T*V/norm(V); % Just setting the thrust parallel to V, adjust to your case.
F_drag = -D/m*V(:);
F_thrust = T(:)/m;
% Calculate the other forces on your particle too
dydt = V; % 
d2ydt2 = [F_thrust + F_drag - g*[0 0 1]]; %  add the forces together
d2ydt2dydt = [d2ydt2; dydt];

HTH