Abstract: In this paper, we propose a full featured and efficient subspace simulation method in the rotation-strain (RS) space for elastic objects. Sharply different from previous methods using the rotation-strain space, except for the ability to handle non-linear elastic materials and external forces, our method correctly formulates the kinetic energy, centrifugal and Coriolis forces which significantly reduces the dynamic artifacts. We show many techniques used in the Euclidean space methods, such as modal derivatives, polynomial and cubature approximation, can be adapted to our RS simulator. Carefully designed experiments show that the equation of motion in RS space has less non-linearity than its Euclidean counterpart, and as a consequence, our method has great advantages of lower dimension and computational complexity than state-of-the-art methods in the Euclidean space.