Hello everybody,
I am starting with Matlab to solve a system of 2 differential equations, second order.
My code is below. It works, but the output is totally wrong.
This code is something taken on matlab help center and adapted to my problem, to help me start.
I have written things in the code "#comment " where it’s not clear to me.
Your help would be very helpful to me.
Thanks a lot in advance.

clear all;
close all;

syms x(t) y(t)

%% Constants
Cd = 0,45 ;% drag coef aircraft [-]
Af = 2 ;% reference area aircraft [-]
m = 10 ;% total mass aircraft [kg]
g = 9.81 ;% acc° of gravity [m/s2]
Teta = 85 ;% launch angle [deg]
V0 = 83 ;% launch velocity [m/s]
rho_Air = 1,2 ;% air density [kg/m3]
t0 = 0; ;% time interval, initial t [s]
tf = 5400 ;% time interval, final t [s]

%% Initial Conditions
x_to = 0 ;% x(t=0)= 0 [m]
dx_t0 = V0*cosd(Teta) ;% x'(t=0)= V0*cosd(Teta) [m/s]
y_to = 0 ;% y'(t=0)= 0 [m]
dy_t0 = V0*sind(Teta) ;% x(t=0)= 0 [m/s]
y0 = [x_to dx_t0 y_to dy_t0 ] ;% vector initial conditions

%% System differential equations to be solved
eq1 = diff(x,2) == -( (Cd*Af*rho_Air)/(2*m) ) * diff(x,1) * (x^2 + y^2)^(1/2)
eq2 = diff(y,2) == – g – ( (Cd*Af*rho_Air)/(2*m) ) * diff(y,1) * ( (diff(x,1))^2 + (diff(y,1))^2 )^(1/2)

%% variables
vars = [x(t); y(t)]

V = odeToVectorField([eq1,eq2])
M = matlabFunction(V,’vars’, {‘t’,’Y’});
% #comment: why the variable x doesn’t appear here ? as I solve on x(t) and
% y(t) -> in V I call eq1 and eq2, then it’s x(t) and y(t)

interval = [t0 tf]; %time interval

ySol = ode45(M,interval,y0);
% #comment: vector y0 containts the boundary conditions for both x and y.
% As here I solve on y, why do we have boundary conditions in x as well ?
% is the function ode capable to make the difference in between boudady
% conditions for x and y ?
tValues = linspace(interval(1),interval(2),1000);
yValues = deval(ySol,tValues,1); %number 1 denotes first position likewise you can mention 2 to 6 for the next 5 positions

plot(tValues,yValues) %if you want to plot position vs time just swap here

% #comment: I need to solve on x as well
% thank you !Hello everybody,
I am starting with Matlab to solve a system of 2 differential equations, second order.
My code is below. It works, but the output is totally wrong.
This code is something taken on matlab help center and adapted to my problem, to help me start.
I have written things in the code "#comment " where it’s not clear to me.
Your help would be very helpful to me.
Thanks a lot in advance.

clear all;
close all;

syms x(t) y(t)

%% Constants
Cd = 0,45 ;% drag coef aircraft [-]
Af = 2 ;% reference area aircraft [-]
m = 10 ;% total mass aircraft [kg]
g = 9.81 ;% acc° of gravity [m/s2]
Teta = 85 ;% launch angle [deg]
V0 = 83 ;% launch velocity [m/s]
rho_Air = 1,2 ;% air density [kg/m3]
t0 = 0; ;% time interval, initial t [s]
tf = 5400 ;% time interval, final t [s]

%% Initial Conditions
x_to = 0 ;% x(t=0)= 0 [m]
dx_t0 = V0*cosd(Teta) ;% x'(t=0)= V0*cosd(Teta) [m/s]
y_to = 0 ;% y'(t=0)= 0 [m]
dy_t0 = V0*sind(Teta) ;% x(t=0)= 0 [m/s]
y0 = [x_to dx_t0 y_to dy_t0 ] ;% vector initial conditions

%% System differential equations to be solved
eq1 = diff(x,2) == -( (Cd*Af*rho_Air)/(2*m) ) * diff(x,1) * (x^2 + y^2)^(1/2)
eq2 = diff(y,2) == – g – ( (Cd*Af*rho_Air)/(2*m) ) * diff(y,1) * ( (diff(x,1))^2 + (diff(y,1))^2 )^(1/2)

%% variables
vars = [x(t); y(t)]

V = odeToVectorField([eq1,eq2])
M = matlabFunction(V,’vars’, {‘t’,’Y’});
% #comment: why the variable x doesn’t appear here ? as I solve on x(t) and
% y(t) -> in V I call eq1 and eq2, then it’s x(t) and y(t)

interval = [t0 tf]; %time interval

ySol = ode45(M,interval,y0);
% #comment: vector y0 containts the boundary conditions for both x and y.
% As here I solve on y, why do we have boundary conditions in x as well ?
% is the function ode capable to make the difference in between boudady
% conditions for x and y ?
tValues = linspace(interval(1),interval(2),1000);
yValues = deval(ySol,tValues,1); %number 1 denotes first position likewise you can mention 2 to 6 for the next 5 positions

plot(tValues,yValues) %if you want to plot position vs time just swap here

% #comment: I need to solve on x as well
% thank you ! Hello everybody,
I am starting with Matlab to solve a system of 2 differential equations, second order.
My code is below. It works, but the output is totally wrong.
This code is something taken on matlab help center and adapted to my problem, to help me start.
I have written things in the code "#comment " where it’s not clear to me.
Your help would be very helpful to me.
Thanks a lot in advance.

clear all;
close all;

syms x(t) y(t)

%% Constants
Cd = 0,45 ;% drag coef aircraft [-]
Af = 2 ;% reference area aircraft [-]
m = 10 ;% total mass aircraft [kg]
g = 9.81 ;% acc° of gravity [m/s2]
Teta = 85 ;% launch angle [deg]
V0 = 83 ;% launch velocity [m/s]
rho_Air = 1,2 ;% air density [kg/m3]
t0 = 0; ;% time interval, initial t [s]
tf = 5400 ;% time interval, final t [s]

%% Initial Conditions
x_to = 0 ;% x(t=0)= 0 [m]
dx_t0 = V0*cosd(Teta) ;% x'(t=0)= V0*cosd(Teta) [m/s]
y_to = 0 ;% y'(t=0)= 0 [m]
dy_t0 = V0*sind(Teta) ;% x(t=0)= 0 [m/s]
y0 = [x_to dx_t0 y_to dy_t0 ] ;% vector initial conditions

%% System differential equations to be solved
eq1 = diff(x,2) == -( (Cd*Af*rho_Air)/(2*m) ) * diff(x,1) * (x^2 + y^2)^(1/2)
eq2 = diff(y,2) == – g – ( (Cd*Af*rho_Air)/(2*m) ) * diff(y,1) * ( (diff(x,1))^2 + (diff(y,1))^2 )^(1/2)

%% variables
vars = [x(t); y(t)]

V = odeToVectorField([eq1,eq2])
M = matlabFunction(V,’vars’, {‘t’,’Y’});
% #comment: why the variable x doesn’t appear here ? as I solve on x(t) and
% y(t) -> in V I call eq1 and eq2, then it’s x(t) and y(t)

interval = [t0 tf]; %time interval

ySol = ode45(M,interval,y0);
% #comment: vector y0 containts the boundary conditions for both x and y.
% As here I solve on y, why do we have boundary conditions in x as well ?
% is the function ode capable to make the difference in between boudady
% conditions for x and y ?
tValues = linspace(interval(1),interval(2),1000);
yValues = deval(ySol,tValues,1); %number 1 denotes first position likewise you can mention 2 to 6 for the next 5 positions

plot(tValues,yValues) %if you want to plot position vs time just swap here

% #comment: I need to solve on x as well
% thank you ! solving ode, ode45, system 2 ode second order MATLAB Answers — New Questions

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