Spacetime Constraints
Computer finds the “best” physical motion satisfying constraints
Example: particle with jet propulsion
 x(t) is position of particle at time t
 f(t) is force of jet propulsion at time t
 Particle’s equation of motion is:


 Suppose we want to move from a to b within t0 to t1 with minimum jet fuel:
subject to x(t0)=a and x(t1)=b