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Theoretically, stars have been formed from the collapse of cores in themolecular clouds. Historically, the core had been assumed as an singularisothermal sphere (SIS), and the collapse had been investigated by aself-similar manner. This is while the rotation and magnetic field lead tonon-symmetric collapse so that a spheroid shape may be occurred. Here, theresultant of the centrifugal force and magnetic field gradient is assumed to bein the normal direction of the rotational axis, and its components are supposedto be a fraction $\beta$ of the local gravitational force. In this research, acollapsing SIS core is considered to find the importance of the parameter$\beta$ for oblateness of the mass shells which are above the head of theexpansion wave. We apply the Adomian decomposition method to solve the systemof nonlinear partial differential equations because the collapse does not occurin a spherical symmetry with self-similar behavior. In this way, we obtain asemi-analytical relation for the mass infall rate $\dot{M}$ of the shells atthe envelope. Near the rotational axis, the $\dot{M}$ decreases with increasingof the non-dimensional radius $\xi$, while a direct relation is observedbetween $\dot{M}$ and $\xi$ in the equatorial regions. Also, the values of$\dot{M}$ in the polar regions are greater than the equatorial values, and thisdifference is more often at smaller values of $\xi$. Overall, the results showthat before reaching the head of expansion wave, the visible shape of themolecular cloud cores can evolve to oblate spheroids. The ratio of major tominor axes of oblate cores increases with increasing the parameter $\beta$, andits value can approach to the apparently observed elongated shapes of cores inthe maps of molecular clouds such as Taurus and Perseus.

Non-similar collapse of singular isothermal spherical molecular cloud cores with nonzero initial velocities