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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:

d

^{2}x/dt

^{2}=-k

^{2}x/r

^{3}

and

d

^{2}y/dt

^{2}=-k

^{2}y/r

^{3}

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 y

_{1}=x and y

_{2}=dy

_{1}/dt

hence, dy

_{2}/dt= -k

^{2}y

_{1}/r

^{3}

and for the second,

let y

_{3}=y and y

_{4}=dy

_{3}/dt

hence, dy

_{4}/dt= -k

^{2}y

_{3}/r

^{3}

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 any one help?