velocity of rocket changing thrust in matlab

To simulate the change in velocity of a rocket under the influence of changing thrust, we can use the following steps using Matlab:

  1. Define the initial conditions of the rocket, such as its mass, initial velocity, thrust, and angle of the rocket's engine.
main.m
% Initial Conditions
m = 1000; % Mass (kg)
v0 = 0; % Initial Velocity (m/s)
t0 = 0; % Initial Time (s)
theta = pi/4; % Angle of rocket's engine with respect to the horizontal
thrust = 10000; % Initial Thrust (N)

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  1. Define the rocket's drag force, which acts in the opposite direction to the rocket's velocity.
main.m
% Drag force
rho_air = 1.225; % Density of air (kg/m^3)
Cd = 0.5; % Drag Coefficient
A = pi*0.5^2; % Cross-sectional area of rocket (m^2)
g = 9.81; % Acceleration due to gravity (m/s^2)

% Define drag force function
fd = @(v) 0.5*rho_air*Cd*A*v^2;

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  1. Define the rocket's acceleration as a function of time. Initially, the rocket will accelerate due to the thrust of the engine, but as the fuel is depleted, the thrust will decrease.
main.m
% Define acceleration function
a = @(t,v) (thrust - fd(v) - m*g*sin(theta))/m;

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  1. Use the ode45 function to solve for the velocity of the rocket as a function of time.
main.m
% Solve for velocity
[t,v] = ode45(a, [t0, 100], v0);

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  1. Plot the results.
main.m
% Plot velocity vs time
plot(t,v)
title('Velocity of Rocket vs Time')
xlabel('Time (s)')
ylabel('Velocity (m/s)')

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The final code implementation for the given problem would look something like this:

main.m
% Define initial conditions
m = 1000; % Mass (kg)
v0 = 0; % Initial Velocity (m/s)
t0 = 0; % Initial Time (s)
theta = pi/4; % Angle of rocket's engine with respect to the horizontal
thrust = 10000; % Initial Thrust (N)

% Define drag force
rho_air = 1.225; % Density of air (kg/m^3)
Cd = 0.5; % Drag Coefficient
A = pi*0.5^2; % Cross-sectional area of rocket (m^2)
g = 9.81; % Acceleration due to gravity (m/s^2)

% Define drag force function
fd = @(v) 0.5*rho_air*Cd*A*v^2;

% Define acceleration function
a = @(t,v) (thrust - fd(v) - m*g*sin(theta))/m;

% Solve for velocity
[t,v] = ode45(a, [t0, 100], v0);

% Plot results
plot(t,v)
title('Velocity of Rocket vs Time')
xlabel('Time (s)')
ylabel('Velocity (m/s)')

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related categories

matlab
physics
simulation

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