This paper is concerned with the development of the theoretical and mathematical background pertinent to the study of steady, corotating solar wind structure in all three spatial dimensions. The dynamical evolution of the plasma in interplanetary space (defined as the region beyond roughly 35 Rs where the flow is supersonic) is approximately described by the nonlinear, single-fluid, polytropic magnetohydrodynamic or hydrodynamic equations. We outline efficient numerical techniques for solving this complex system of coupled, hyperbolic partial differential equations. The present forumulation is inviscid and nonmagnetic, but our methods allow for the potential inclusion of both features with only modest modifications. We examine one simple, highly idealized hydrodynamic model stream to illustrate the fundamental processes involved in the three-dimensional dynamics of stream evolution. We find that spatial variations in the rotational stream interaction mechanism produce small nonradial flows on a global scale that lead to the transport of mass, energy, and momentum away from regions of relative compression and into regions of relative rarefaction. The magnitude of this transport is small, but inside 1 AU the nonradial flow can significantly retard shock formation by allowing fluid in the compressions to slip laterally, thereby partially relieving the stresses built up in the stream interaction. Comparison with simpler models demonstrates the essential nonlinear, multidimensional nature of the interplanetary dynamics. A subsequent paper will be devoted to the investigation of a wide range of more realistic model streams.