We present two methods for characterization of motional-mode configurations that are generally applicable to the weak and strong-binding limit of single or multiple trapped atomic ions. Our methods are essential to realize control of the individual as well as the common motional degrees of freedom. In particular, when implementing scalable radio-frequency trap architectures with decreasing ion-electrode distances, local curvatures of electric potentials need to be measured and adjusted precisely, e.g., to tune phonon tunneling and control effective spin-spin interaction. We demonstrate both methods using single 25 Mg + ions that are individually confined 40 µm above a surface-electrode trap array and prepared close to the ground state of motion in three dimensions. [14], yielding increasing interaction strengths by decreasing system length scales. Correspondingly, higher-order terms need to be considered, in order to enable precise control of interaction potentials. For example, in microfabricated surface-electrode ion trap arrays [15-17] local potentials, dominated by applied electric trapping potentials, define motional modes. For envisioned quantum simulations, motional degrees of freedom can be exploited either within individual sites or between different sites. This, in turn, requires adjustment of motional-mode configurations, i.e., individual orientation of the normal-mode vectors and related motional frequencies, to enable individual, tunable inter-site interactions [17]. In this letter, we introduce and experimentally demonstrate two distinct methods for the analysis of motional-mode configurations that are generally applicable to the weak and strong-binding limit. For the latter, we cool single ions close to the ground state of motion in three dimensions.To introduce our system, we consider a single ion with charge Q and mass m, harmonically bound in three di-