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I have some trouble while trying to use the Poincare method in a free fall problem.

There's some point on earth, that the vector R_{0}points at. from this point there is an orthonormal coordinate system, and some point of mass at (R_{x}, R_{y}, R_{z}).

I found the expression for the sum of Coriolis force, the gravity force and the centrifugal force. Though, in this expression, the expression of every component includes a mixture of R_{x/y/z}, so I can't just say that it's a function ofR, and say thatR=[tex]\epsilon[/tex]R+[tex]\epsilon^2[/tex]_{1}R+[tex]\epsilon^3[/tex]_{2}R+..._{3}

and substitute it in the expression of the force.

My aim is to express the acceleration, and say that [tex]\ddot x = a[/tex], substitute, and compare between the coefficients of the same powers of [tex]\epsilon[/tex].

Any idea how to do that...? I'm at a loss.

Thanks!

P.S. the expression I've got for the x component of the acceleration, for example, is:

[tex]\ddot x = \frac{GM}{\vert \mathbf{R}+\mathbf{R_0 }\vert}\mathbf{R_x} + \frac{\omega^2}{2}\sin{(2\phi)}\mathbf{R_y} -\omega^2\sin^2{(\phi)}\mathbf{R_x}[/tex]+2\omega\dot\mathbf{R_z}\sin{(\phi)}

(For some reason it doesn't include the last part, outside of the tex tags, if I put it between the tags. I think there's a size limit...)

Thanks again.

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# Homework Help: Perturbation Theory - Poincare Method

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