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 before his death. These three books, "Caliban", "Inferno" and "Utopia", introduce a new set of the Three Laws. The so-called New Laws are similar to Asimov's originals with the following differences: the First Law is modified to remove the "inaction" clause, the same modification made in "Little Lost Robot"; the Second Law is modified to require cooperation instead of obedience; the Third Law is modified so it is no longer superseded by the Second (i.e., a "New Law" robot cannot be ordered to destroy itself); finally, Allen adds a Fourth Law which instructs the robot to do "whatever it likes"