MATLAB: Movements of the descent vehicle in the atmosphere of Earth

homework

I need help writting a Matlab script file, In the matlab I need to write the equations of motion of the space capsule that are as follows:

and I need the graph of time (x axis) vs speed (y axis).

Best Answer

You have four differential equations involving four variables: V, theta, H, and L. You have to solve these simultaneously since they depend on each other. You can't just pick the one you want and try to solve it by itself like this:

f = @(t,v) v*sind(theta);

You need an f that takes in a 4-element state vector containing V, theta, H, and L, and produces a 4-element derivative vector containing dV/dt, dtheta/dt, dH/dt, and dL/dt. Then that is used in your RK4 looping code.

Related Solutions

MATLAB: Solve equations of Motion using Matlab ODE45

You will have a 4-element state vector instead of 2.

initial_cond = [1;1;0;0];
[t,y] = ode45(@(t,y)ODE_funct_fourth_order(t, y, m1, m2, L, k, g),tspan,initial_cond);

with

function dydt = ODE_funct_fourth_order(t, y, m1, m2, L, k, g)
    dydt = [y(3);y(4);something;something];
end

where y is

y(1) = x

y(2) = theta

y(3) = xdot

y(4) = thetadot

You get the expressions for dydt(3) and dydt(4) by solving (e.g. on paper or inside your derivative function using backslash \ operator) your matrix equations for xdotdot and thetadotdot.

MATLAB: How to calculate the jumper’s final distance on this problem

function dist=BJump(v,theta,rho,s)
    x=0;
    g=9.81;
    c=.72;
    dt=.000001;%not sure how accurate you need
    y=v*sin(theta)*dt;
    while y>1e-7
        dTheta=-g*cos(theta)*dt/v;
        dv=(c*rho*s/2-g*sin(theta))*dt;
        x=v*cos(theta)*dt+x;
        v=v+dv;
        theta=theta+dTheta;
        y=y+v*sin(theta);
    end
    dist=x;
end

When I run this:

d=BJump(10,pi/8,.94,.5);%I get d=7.2748

Best Answer

Related Solutions

MATLAB: Solve equations of Motion using Matlab ODE45

MATLAB: How to calculate the jumper’s final distance on this problem

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