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

In this paper, we present a new public code, named ynogkm (Yun-Nan observatories geodesic in a Kerr-Newman spacetime for massive particles), for the fast calculation of time-like geodesics in the Kerr-Newman (K-N) spacetime, which is a direct extension of ynogk (Yun-Nan observatories geodesic Kerr) 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.