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 to understand when they are causing pain or injury and know to stop. Many are constructed with physical safeguards such as bumpers, warning beepers, safety cages, or restricted-access zones to prevent accidents. Even the most complex robots currently produced are incapable of understanding and applying the Three Laws; significant advances in artificial intelligence would be needed to do so, and even if AI could reach human-level intelligence, the inherent ethical complexity as well as cultural/contextual dependency of the laws prevent them from being a good candidate to formulate robotics design constraints. However, as the complexity of robots has increased, so