Equations of motion when masses move according to Newton's law of gravity. In general relativity, rotational motion is described by the relativistic angular momentum tensor, including the spin tensor, which enter the equations of motion under covariant derivatives with respect to proper time. The Mathisson–Papapetrou–Dixon equations describe the motion of spinning objects moving in a gravitational field. Unlike the equations of motion for describing particle mechanics, which are systems of coupled ordinary differential equations, the analogous equations governing the dynamics of waves and fields are always partial differential equations, since the waves or fields are functions of space and time. For a particular
Three Laws of Robotics robot's entire developing consciousness is based. This concept is largely fuzzy and unclear in earlier stories depicting very rudimentary robots who are only programmed to comprehend basic physical tasks, where the Three Laws act as an overarching safeguard, but by the era of "The Caves of Steel" featuring robots with human or beyond-human intelligence the Three Laws have become the underlying basic ethical worldview that determines the actions of all robots. In the 1990s, Roger MacBride Allen wrote a trilogy which was set within Asimov's fictional universe. Each title has the prefix "Isaac Asimov's" as Asimov had approved Allen's outline