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 settlers on new Spacer worlds may lead to the robots seeing themselves as the true humans, and deciding to keep the worlds for themselves rather than allow the Spacers to settle there. "—That Thou Art Mindful of Him", which Asimov intended to be the "ultimate" probe into the Laws' subtleties, finally uses the Three Laws to conjure up the very "Frankenstein" scenario they were invented to prevent. It takes as its concept the growing development of robots that mimic non-human living things and given programs that mimic simple animal behaviours which do not require the Three Laws. The presence of