System for analyzing the motions of a mechanical structure, comprising: (a) accelerometers provided as standard accelerometers to measurement-points of said mechanical structure, (b) at least three accelerometers provided as reference accelerometers to measurement-points of said mechanical structure, (c) at least one shaker being attached to said mechanical structure for moving the structure periodically within a first frequency range, further comprising at least one data processing system being configured to: (d) receiving measurements from said accelerometers at the measurement-points when periodically moving the structure within said first frequency range by said at least one shaker, said system being characterized by said at least one data processing system further is configured to calibrate the accelerometers' positions and orientations by the following steps: (e) determining from said measurements of said at least three reference accelerometers rigid body motions, (f) determining positions and orientations of accelerometers from said rigid body motions, wherein step (f), further comprises: decomposing the 6 rigid body motions applying an infinitesimal rotation model into six infinitesimal rigid body translation-rotation pairs by solving a resulting set of linear equations using a solver, linearly recombining said six infinitesimal rigid body translation-rotation pairs into three pure translations, deriving orientations of accelerometers from said three pure translations, deriving positions of accelerometers from said 6 rigid body motions. (a) accelerometers provided as standard accelerometers to measurement-points of said mechanical structure, (b) at least three accelerometers provided as reference accelerometers to measurement-points of said mechanical structure, (c) at least one shaker being attached to said mechanical structure for moving the structure periodically within a first frequency range, further comprising at least one data processing system being configured to: (d) receiving measurements from said accelerometers at the measurement-points when periodically moving the structure within said first frequency range by said at least one shaker, said system being characterized by said at least one data processing system further is configured to calibrate the accelerometers' positions and orientations by the following steps: (e) determining from said measurements of said at least three reference accelerometers rigid body motions, (f) determining positions and orientations of accelerometers from said rigid body motions, wherein step (f), further comprises: decomposing the 6 rigid body motions applying an infinitesimal rotation model into six infinitesimal rigid body translation-rotation pairs by solving a resulting set of linear equations using a solver, linearly recombining said six infinitesimal rigid body translation-rotation pairs into three pure translations, deriving orientations of accelerometers from said three pure translations, deriving positions of accelerometers from said 6 rigid body motions. (e) determining from said measurements of said at least three reference accelerometers rigid body motions, (f) determining positions and orientations of accelerometers from said rigid body motions, wherein step (f), further comprises: decomposing the 6 rigid body motions applying an infinitesimal rotation model into six infinitesimal rigid body translation-rotation pairs by solving a resulting set of linear equations using a solver, linearly recombining said six infinitesimal rigid body translation-rotation pairs into three pure translations, deriving orientations of accelerometers from said three pure translations, deriving positions of accelerometers from said 6 rigid body motions. decomposing the 6 rigid body motions applying an infinitesimal rotation model into six infinitesimal rigid body translation-rotation pairs by solving a resulting set of linear equations using a solver, linearly recombining said six infinitesimal rigid body translation-rotation pairs into three pure translations, deriving orientations of accelerometers from said three pure translations, deriving positions of accelerometers from said 6 rigid body motions.