A method is disclosed for applying physics-based simulation to an animator provided rig. The disclosure presents equations of motions for simulations performed in the subspace of deformations defined by an animator's rig. The method receives an input rig with a plurality of deformation parameters, and the dynamics of the character are simulated in the subspace of deformations described by the character's rig. In certain embodiments, the present disclosure provides a method that transforms stiffness values defined on rig parameters to a non-homogeneous distribution of material parameters for the underlying rig.