Abstract: This paper presents a spectral approach to compress dynamic animation consisting of a sequence of homeo-morphic manifold meshes. Our new approach directly compresses the field of deformation gradient defined on the surface mesh, by decomposing it into rigid-body motion (rotation) and non-rigid-body deformation (stretching/shearing) through polar decomposition. It is known that the Rotation Group has the algebraic topology of 3-D ring, which is different from other operations like stretching and shearing. Thus we compress these two groups separately, by using Manifold Harmonics Transform to drop out their high-frequency details. Our experimental result shows that our method achieves a good balance between the reconstruction quality and compression ratio. We compare our results quantitatively with other existing approaches on animation compression, using standard measurement criteria.