The precession of orbital plane and the significant variabilities of binary pulsars

There are two kinds of expressions on the precession of orbital plane of a binary pulsar system, which are given by Barker $&$ O'Connell (1975) and Apostolatos et al. (1994), Kidder (1995) respectively. This paper points out that these two kinds of orbital precession velocities are actually obtained by the same Lagrangian under different degrees of freedom. Correspondingly the former expression is not consistent with the conservation of the total angular momentum vector; whereas the latter one is. Damour $&$ Sch\"afer (1988) and Wex $&$ Kopeikin (1999) have applied Barker $&$ O'Connell's orbital precession velocity in pulsar timing measurement. This paper applies Apostolatos et al. $&$ Kidder's orbital precession velocity in pulsar timing measurement. We analyze that Damour $&$ Sch\"afer's treatment corresponds to negligible Spin-Orbit induced precession of periastron. Whereas the effects corresponding to Wex $&$ Kopeikin and this paper are both significant (however they are not equivalent). The observational data of two typical binary pulsars, PSR J2051-0827 and PSR J1713+0747 apparently support significant Spin-Orbit coupling effect. Further more, the discrepancies between Wex $&$ Kopeikin and this paper can be tested on specific binary pulsars with orbital plane nearly edge on. If the orbital period derivative of double-pulsar system PSRs J0737-3039 A and B, with orbital inclination angle $i=87.7_{-29}^{+17}$deg, is much larger than that of the gravitational radiation induced one, then the expression of this paper is supported, otherwise Wex $&$ Kopeikin's expression is supported.