Orbit of satellite 2nd order ODE using Matlab

[olski1]

Hi,

I am completely stuck on this problem that has been given to us.

I must solve a set of 2nd order differential equations using Euler's method. It is for a geosychronous orbit of a satellite, meaning the orbit is circular and the velocity vector is perpendicular to the radius vector (r.V=0). The equations are:

d²x/dt²=-k²x/r³

and

d²y/dt²=-k²y/r³

k^2,r and V are all given.

My first step was to set up sets of ode's to solve.

for the first equation we have,

let y₁=x and y₂=dy₁/dt

hence, dy₂/dt= -k²y₁/r³

and for the second,

let y₃=y and y₄=dy₃/dt

hence, dy₄/dt= -k²y₃/r³

which I think is correct.

Now I have to pass this into a MATLAB function which uses eulers method. But I have no idea how to implement it. my main problem at the moment is that I do not know what to use as my initial y_1,2,3,4 values in the function vector.

Can anyone help?

 

[voko]

I am not sure why anyone would want to solve and ODE for motion which is completely known, but still.

You can take any initial position as long as it is on the orbit (circle). The velocity, as you say, is perpendicular to it and must be equal to the length of the orbit divided by one sidereal day.