1. A method, comprising: using a computer to perform operations comprising: receiving input defining a trajectory of an animated character as a goal constraint during execution of an interactive application; receiving input representing one or more external forces acting on the animated character during execution of the interactive application, a root of the animated character being unactuated by the one or more external forces; determining a reference pose for the animated character in a current animation frame in reaction to the one or more external forces, said determining comprising performing a quasi-physical simulation, the quasi-physical simulation being expressed as a linear system enforcing the goal constraint for the horizontal components of a center of mass of the animated character by performing operations comprising: determining joint torques to minimize an addition of a non-physical force at the root of the animated character, the joint torques being determined based on a torque objective; determining the non-physical force to apply to the root of the animated character to enforce the goal constraint, the determining the non-physical force not being constrained by the laws of physics simulated in the quasi-physical simulation and the goal constraint being expressed as a linear function of joint accelerations; adding the determined non-physical force to the root of the animated character; and displaying the animated character in its determined pose.