Matlab Coding for a spacecraft

[James Tursa]

We are reluctant to open a pdf file. Please post your question as clear text.

[Musama Chilekwa]

Sorry the question has certain figures I can’t post in text

[John D'Errico]

The problem is, this is just your homework assignment. We cannot just give you code to do your work, when no effort is even shown on your part.

Answer 1

[James Tursa]

Thanks for the image post. So, this is a standard orbital proximity operations relative motion question. The equations in your question are known as the Clohessy-Wiltshire Equations. You can research that on the web. These have a closed form solution. Not knowing how much help is allowed for this homework question, I will simply point you to a website that has some information on it:

https://en.wikipedia.org/wiki/Clohessy%E2%80%93Wiltshire_equations

The variable names in this link are switched from yours ... x is y and y is x. So you will have to deal with that.

What are you supposed to do for your homework? Solve the differential equations on paper and show your work? Use an integration scheme such as ode45( ) or your own hand-coded RK4 integrator to solve it numerically? Or ...?

To answer the question about periodic orbits that return you to the exact starting point, I would direct your attention to any parts of the solution that contain secular terms (terms with "t" in them that are not inside a sin( ) or cos( ) function). Ask yourself what restrictions there must be on the initial conditions in order for the coefficients on these terms to combine to be 0?