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 unusual fractal construction of his positronic brain. In his dream the first two Laws are absent and the Third Law reads "A robot must protect its own existence". Asimov took varying positions on whether the Laws were optional: although in his first writings they were simply carefully engineered safeguards, in later stories Asimov stated that they were an inalienable part of the mathematical foundation underlying the positronic brain. Without the basic theory of the Three Laws the fictional scientists of Asimov's universe would be unable to design a workable brain unit. This is historically consistent: the occasions where roboticists modify