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 person capable of circumventing the safeguards and forcing the robot into a brain-destroying paradox. In "Robots and Empire", Daneel states it's very unpleasant for him when making the proper decision takes too long (in robot terms), and he cannot imagine being without the Laws at all except to the extent of it being similar to that unpleasant sensation, only permanent. Robots and artificial intelligences do not inherently contain or obey the Three Laws; their human creators must choose to program them in, and devise a means to do so. Robots already exist (for example, a Roomba) that are too simple