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 so long as this does not conflict with the first three laws. The philosophy behind these changes is that "New Law" robots should be partners rather than slaves to humanity, according to Fredda Leving, who designed these New Law Robots. According to the first book's introduction, Allen devised the New Laws in discussion with Asimov himself. However, the "Encyclopedia of Science Fiction" says that "With permission from Asimov, Allen rethought the Three Laws and developed a new set,". Jack Williamson's novelette "With Folded Hands" (1947), later rewritten as the novel "The Humanoids", deals with robot servants whose prime directive is