Symbolic approach for the applicability of the third integral of motion

الملخص EN

In the present paper, literal analytical solutions in recurrent power series forms are developed for the plane motion in an axisymmetric potential to study the applicability of the third integral of motion.

For the computational developments of these solutions, efficient method using continued fraction theory together with the device of interval division are provided.

Moreover some numerical and graphical illustrations are also given.

It was found that, the third integral of motion exists for only a limited range of initial conditions.

But it may exist whatever the time interval may be, if it's initial value£(O,O,12).