Correcting for the dynamical effects in the observed second derivative of the spin frequency.

The observed value of the second time-derivative of the spin frequency contains contribution from various dynamical terms. We derive expressions for all the individual terms expressible in terms of the Galactic coordinates, the proper motion in respective Galactic coordinates, the pulsar distance and the radial velocity. We explore the contribution of these terms near the Galactic Centre. We also provide the expected distribution of the magnitude of the individual terms resulting from the Monte Carlo simulations. We discuss the use of our methods to calculate a realistic value of the braking index using the intrinsic second derivative of the spin frequency that we obtain.