Inverse synthetic aperture radar (ISAR) imaging is an extension of synthetic aperture radar (SAR) imaging to cases where the synthetic aperture is produced by target motion (trajectory), as opposed to radar motion, and hence unknown a priori. In SAR knowledge of the motion is used to produce the image; lack of this knowledge causes the ISAR imaging problem to be underdetermined. Additional constraints are needed to obtain a solution. The typical constraint used, to assume that the target is effectively rotating at a constant angular velocity, can faithfully image the target only in those cases where the real trajectory is accurately described by this assumption. We show that ISAR imaging can be extended to include much more general trajectories by putting constraints on the image produced rather than on the trajectory. The work we present includes (1) a theoretical analysis of ISAR image formation with arbitrary trajectories, (2) computer verification of this analysis and simulation of our method, (3) sonar imaging of simple objects, and (4) an optical implementation of our method.