Ynogkm: A new public code for calculating time-like geodesics in the Kerr-Newman spacetime

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In this paper we present a new public code, named $ynogkm$, for the fast calculation of time-like geodesics in the Kerr-Newmann (K-N) spacetime, which is a direct extension of $ynogk$ calculating null geodesics in a Kerr spacetime. Following the strategies used in $ynogk$, we also solve the equations of motion analytically and semi-analytically by using Weierstrass' and Jacobi's elliptic functions and integrals, in which the Boyer-Lidquist (B-L) coordinates $r$, $\theta$, $\phi$, $t$ and the proper time $\sigma$ are expressed as functions of an independent variable $p$ (Mino time). All of the elliptic integrals are computed by Carlson's elliptic integral method, which guarantees the fast speed of the code. Finally the code is applied to a couple of toy problems.