Research in nonlinear modal analysis deals with the extension of linear modes to nonlinear mechanical systems. eigenmanifolds are a recent addition to this field. Pursuing a geometrical viewpoint, they generalize modes to nonlinear mechanical systems with non-constant inertia tensors (e.g., robots, biomechanical models). This work aims at shading light on the connection between this new definition and the well-known extended Rosenberg modes. A key feature of extended Rosenberg modes is that all the associated modal oscillations must intersect at the same point. This appears to be a robust property of oscillations arising when the inertia tensor is constant (Euclidean case).
Nevertheless, this symmetry is soon broken when the tensor is configuration-dependent. This paper provides sufficient conditions for this property to be conserved in the non-Euclidean domain, establishing a bridge between the Rosenberg theory and eigenmanifolds. The condition appears to be tight since violating it meant to lose the symmetry in all the tested cases.