Euler's laws of motion each governed by Newton’s laws of motion, then Euler’s equations can be derived from Newton’s laws. Euler’s equations can, however, be taken as axioms describing the laws of motion for extended bodies, independently of any particle distribution. The total body force applied to a continuous body with mass , mass density , and volume , is the volume integral integrated over the volume of the body: where is the force acting on the body per unit mass (dimensions of acceleration, misleadingly called the "body force"), and is an infinitesimal mass element of the body. Body forces and contact forces acting
Three Laws of Robotics robots and therefore lacking the Three Laws. The robot conspirators see the Trantorian tiktoks as a massive threat to social stability, and their plan to eliminate the tiktok threat forms much of the plot of "Foundation's Fear". In "Foundation's Triumph" different robot factions interpret the Laws in a wide variety of ways, seemingly ringing every possible permutation upon the Three Laws' ambiguities. Set between "The Robots of Dawn" and "Robots and Empire", Mark W. Tiedemann's "Robot Mystery" trilogy updates the "Robot"–"Foundation" saga with robotic minds housed in computer mainframes rather than humanoid bodies. The 2002 Aurora novel has robotic characters