Physics-based animation programs are important in a variety of contexts, including education, science and entertainment among others. Manual construction of such programs is expensive, time consuming and prone to error. We have developed a system for automatically synthesizing physics-based animation programs for a significant class of problems: constrained systems of rigid bodies, subject to driving and dissipative forces. Our system includes a graphical interface for specifying a physical scenario, including objects, geometry, dynamical variables and coordinate systems, along with a symbolic interface for specifying forces and constraints operating in the scenario. The entities defined in the graphical interface serve as the underlying vocabulary for specifications constructed in the symbolic interface. We use an algorithmically controlled rewrite system to construct a numerical simulation program that drives a real-time animation of the specified scenario. The algorithm operates by partitioning the constraints and dynamic variables into classes, assigning each class to be implemented in a different component of a general simulation program scheme. Our approach provides many of the benefits of formal deductive methods of program synthesis, while keeping the computational costs of program synthesis more in line with conventional program generator technology. We have successfully tested our system on numerous examples.