Asked by Bilal Arshed
on 22 Nov 2019 at 13:31

Hi,

Im trying to plot a complete 2*pi orbit 500km about the earth. I have the code i am using shown below but it ends up plotting a cosine function as the tangent velocity remains only positive. I am pretty sure the rest of the code is fine.

I need hlep either convering a cosine plot into a circular plot or help ensuring the the velocity of the vehicle changes from + to - at pi.

I have also attached the mathamatical reentry dynamics equations

% myeqn file - script 1

function dv = myeqn(t, x)

alpha = 0; % starting AoA

%State vector, intial conditions deifined in run_myeqn

theta=x(4); %starting theta angle

r=x(3); %starting postion above earth

v_t=x(2); % tanget velocity

v_r=x(1); % radial velocity

gamma = tan(x(1)./x(2));

v=sqrt(v_t^2+v_r^2); % velocity vector

mu_e = 3.986e14;

Re=6371e3;

h = r-Re;

m=5000;

%[T, P, rho] = standard_atm(h);

%lift drag set to zero as we are only trying to orbit the earth. therefore no drag and lift.

L=0;

D=0;

%[L, D] = Lift_Drag(h, alpha, v, rho);

dv_r = (-(mu_e)/(r^2)) + ((v_t^2)/r) + ((1/m)*(-D*sin(gamma)+L*cos(gamma))); % radial accel equation

dv_t= -((v_r*v_t)/r) + 1/m*(-D*cos(gamma) - L*sin(gamma)); % tangent accel equation

dr = v_r;

dtheta = v_t/r;

dv=[dv_r dv_t dr dtheta]';

return

%run_myeqn - script 2

clc

clear

v0=[0, 7616.6, 6871e3, 0];

t0=0;

tend=5000;

tstep=1;

options=odeset('Events',@myEvent);

[t,v] = ode45(@myeqn, t0:tstep:tend, v0,options)

r = v(:,3);

theta = v(:,4);

v_t = v(:,2);

v_r = v(:,1);

plot (r, theta)

%hold on

%ang=0:0.01:2*pi;

%x2=6871e3*cos(ang);

%y2=6871e3*sin(ang);

%plot(x2, y2);

Answer by Steven Lord
on 22 Nov 2019 at 14:34

Accepted Answer

Instead of a plot I think you want a polarplot (assuming you're using release R2016a or later.)

Bilal Arshed
on 22 Nov 2019 at 14:47

yeah im on R2019a! i tried polar plot and it worked but seems to spiral into the earth now. I have attached an image of it.

UPDATED: thanks i acutally managed to fix it, but suggesting a polarplot really helps!

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