The paper introduces a new method for creating character animation called spacetime constraints. This method allows animators to specify what the character needs to do, how the motion should be performed, the character's physical structure, and the physical resources available. The solution to the problem of constrained optimization, which combines the animator's requirements with Newton's laws, results in physically valid and realistic motion. The authors demonstrate this approach using a Luxo lamp as an example, showing that the method can produce coordinated motions that exhibit traditional animation principles such as anticipation, squash-and-stretch, follow-through, and timing. The paper also discusses the numerical solution of large constrained optimization problems and the development of an object-oriented symbolic algebra system to automate the setup of these problems. The results show that spacetime methods can produce complex and realistic motion with minimal kinematic constraints, offering a more economical and powerful means of control compared to traditional keyframing.The paper introduces a new method for creating character animation called spacetime constraints. This method allows animators to specify what the character needs to do, how the motion should be performed, the character's physical structure, and the physical resources available. The solution to the problem of constrained optimization, which combines the animator's requirements with Newton's laws, results in physically valid and realistic motion. The authors demonstrate this approach using a Luxo lamp as an example, showing that the method can produce coordinated motions that exhibit traditional animation principles such as anticipation, squash-and-stretch, follow-through, and timing. The paper also discusses the numerical solution of large constrained optimization problems and the development of an object-oriented symbolic algebra system to automate the setup of these problems. The results show that spacetime methods can produce complex and realistic motion with minimal kinematic constraints, offering a more economical and powerful means of control compared to traditional keyframing.