We present an updated version of the Motion4D-library that can be used for the newly developed GeodesicViewer application. New version program summary Program title: Motion4D-library Catalogue identifier: AEEX_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEEX_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 153 757 No. of bytes in distributed program, including test data, etc.: 5 178 439 Distribution format: tar.gz Programming language: C++ Computer: All platforms with a C++ compiler Operating system: Linux, Unix, Windows RAM: 31 MBytes Catalogue identifier of previous version: AEEX_v1_0 Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 2355 Classification: 1.5 External routines: Gnu Scientific Library (GSL) ( http://www.gnu.org/software/gsl/) Does the new version supersede the previous version?: Yes Nature of problem: Solve geodesic equation, parallel and Fermi–Walker transport in four-dimensional Lorentzian spacetimes. Solution method: Integration of ordinary differential equations. Reasons for new version: To be applicable for the GeodesicViewer (accepted for publication in Comput. Phys. Comm. (COMPHY) 3941, doi:10.1016/j.cpc.2009.10.010 [program AEFP_v1_0]), there were several minor adjustments to be done. Summary of revisions: 1. Calculation of embedding diagrams are improved. 2. Physical units can be used for some metrics. 3. Tests for the constraint equation within the metric classes are slightly modified. 4. New metrics: AlcubierreWarp, GoedelScaled, GoedelScaledCart, Kasner. Running time: The test runs provided with the distribution require only a few seconds to run.