The comprehensive simulation of flexible multibody systems calls for the ability to model various types of structural components such as rigid bodies, beams, plates, and kinematic joints. Modal components test offer additional modeling versatility by enabling the treatment of complex, three-dimensional structures via modal reduction procedures based on the small deformation assumption. In this paper, the problem is formulated within the framework of the motion formalism. The kinematic description involves simple, straightforward frame transformations and leads to deformation measures that are both objective and tensorial. Derivatives are expressed in the material frame, which results in the remarkable property that the tangent matrices are independent of the configuration of the modal component with respect to an inertial frame. This implies a reduced level of geometric nonlinearity as compared to standard description. In particular, geometrically nonlinear problems can be solved with the constant tangent matrices of the reference configuration, without re-evaluation and re-factorization.