This paper presents a spectral approach to compress dynamic animation consisting of a sequence of homeomor-phic 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) through polar decompo-sition. It is known that the rotation group has the algebraic topology of 3D ring, which is different from other operations like stretching. Thus we compress these two groups separately, by using Manifold Harmonics Transform to drop out their high-frequency details. Our experimental result shows that the proposed method achieves a good balance between the reconstruction quality and the compression ratio. We compare our results quantitatively with other existing approaches on animation compression, using standard measurement criteria.