Plotting ode 45 results

Matlab 2020B was used to draft code:

Question

Drafted Code:

function [f] = twobody (t,X)

% Designed to call two body eqautions of motion

%x(1)= x position;

%x(2)= y position;

%x(3) = z position;

%x (4) = x velocity;

%x (5) = y velocity;

%x (6) = z velocity;

mu = 398600; % km^3/s^2

f = zeros (size(X));

Xdot(1:3) = X (4:6);

r=norm(X(1:3));

Xdot(4:6)= (-mu/r^3)*X(1:3);

end

Script file:

R0 = [6510.75956901532 2676.16546382759 333.33402937319]; %km. Transpose of column matrix

V0 = [-2.23202460862428 9.49860960555864 1.18311436869621]; % Km/s. Transpose of column matrix

X0= [R0,V0]; % Column vector input to ODE45

options=odeset; options = odeset('RelTol',1e-12,'AbsTol', 1e-12);

t = [0:10:86400]; % 24hrs converted to sec with 10 sec step size

[t,X]=ode45(@twobody,t,X0,options);

clear all

plot(t,R0);

xlabel('Time(seconds)');

ylabel('Radius (Km)');

Error message:

Unrecognized function or variable 't'.

Error in twobodyscript (line 9)

plot(t,R0);

Can someone help resolve the error message and help plot the three plots? and i am not sure how to approach below question yet, some help would be greatly appreciated.

[Stephen23]

Note that inside your function the output f is always just an array of zeros, while the variable Xdot is totally unused.

Answer 1

[Stephen23]

clear all % <- get rid of this.

It seems that the main purpose of CLEAR ALL is to introduce bugs into beginners' code when they use it totally inappropriately, e.g. at the start of every script or in the middle of their code:

https://en.wikipedia.org/wiki/Anti-pattern

[imran shaikh]

Hi Stephen,

Thank you, variable 't' issue was resolved.

but another error popped up as follows:

>> twobodyscript

Error using plot

Vectors must be the same length.

Error in twobodyscript (line 8)

plot(t,R0);

I imagine this is because time t is from 0 to 86400 and R0 is only three numbers. Any idea on how to resolve that?

[Stephen23]

"I imagine this is because time t is from 0 to 86400 and R0 is only three numbers"

Yes.

"Any idea on how to resolve that?"

Not really, because you did not explain what you expect to happen when you try to plot different numbers of X and Y values.

[Stephen23]

Making a few guesses about the meaning of your variables, perhaps something like this:

R0 = [6510.75956901532,2676.16546382759,333.33402937319];   % km
V0 = [-2.23202460862428,9.49860960555864,1.18311436869621]; % Km/s
Op = odeset('RelTol',1e-12,'AbsTol', 1e-12);
ts = 0:10:86400; % 24hrs converted to sec with 10 sec step size
[t,Y] = ode45(@twobody,ts,[R0,V0],Op);
plot(t,Y(:,1:3));
ylabel('Radius (km)');
xlabel('Time (seconds)');

function Xdot = twobody (t,X)
mu = 398600; % km^3/s^2
Xdot = zeros(size(X));
Xdot(1:3) = X(4:6);
r = norm(X(1:3));
Xdot(4:6)= (-mu/r^3)*X(1:3);
end