simulate an object thrown with drag force using ode45 in matlab

To simulate an object thrown with drag force in Matlab, we can use the ODE45 solver. ODE45 is a numerical solver for initial value problems of ordinary differential equations.

Here's an example of how to simulate an object thrown with drag force using ODE45:

main.m
% Define constants
g = 9.81;               % acceleration due to gravity
rho = 1.2;              % density of fluid (in this case air)
Cd = 0.5;               % drag coefficient
A = pi*(0.1)^2;         % cross-sectional area of object
m = 0.1;                % mass of object
v0 = [10; 5];           % initial velocity (m/s)

% Define the drag force
D = @(v) 0.5*rho*Cd*A*norm(v)*v;

% Define the ODE system
f = @(t,v) [0; -g] - (D(v)/m);

% Define the time span and initial conditions
tspan = [0, 10];
y0 = [0; 0; v0];

% Solve the ODE system using ODE45
[t, y] = ode45(f, tspan, y0);

% Plot the trajectory
plot(y(:,1), y(:,2));
xlabel('x (m)');
ylabel('y (m)');
title('Trajectory of Object Thrown with Drag Force');
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In this example, we first define the constants of the problem, including the acceleration due to gravity, the density of the fluid (in this case air), the drag coefficient, the cross-sectional area of the object, the mass of the object, and the initial velocity.

We then define the drag force as a function of velocity using the drag equation. Next, we define the ODE system that describes the motion of the object, including the force due to gravity and the drag force.

We then define the time span and initial conditions for the simulation, and use ODE45 to solve the ODE system. Finally, we plot the trajectory of the object using the x and y components of its position vector.