  The dynamical characterization of the Millisecond Pulsar (MSP) parameters is
a key issue in understanding these systems. We present an analytical analysis
of the orbital parameters of binary MSPs with long periods (Porb > 2 d) and
circular (e < 0.1) orbits, produced by an asymmetric kick model imparted during
the Accretion Induced Collapse (AIC) of white dwarfs process. It turns out that
the distribution of orbits peaks up to P_orb;f < 90 d with strong
circularization. Considering the different assumptions about the distribution
of companions He stars 3M< Mcom < 5M, the binary will affect the setups of the
balance condition of minimum energy. Our analytical approach is just the first
approach to the more complete models required for describing all binary
parameters after an asymmetric kick. Therefore, we have also run some numerical
simulations in order to compare their results with the analytical studies. We
aim to initiate the first exploration of the full complexity of the problem,
when combining a variable kick time and a variable kick vector direction.
Indeed, the numerical simulations show patterns resembling the complex behavior
found in chaotic scattering problems. Although we deal with a deterministic
problem and bounded orbits, the regular characteristic orbits are found in more
realistic phases during the AIC process. In addition, the overall process can
show complex behaviors strongly associated with the internal kick mechanisms.
This would lead us to identify the nature of regular orbits and their orbital
morphology.
