History of variational principles in physics involves integrals over an interval of time and (for fields) extended region of space. Moreover, in the usual formulation of classical action principles, the initial and final states of the system are fixed, e.g., In particular, the fixing of the "final" state appears to give the action principle a teleological character which has been controversial historically. This apparent teleology is eliminated in the quantum mechanical version of the action principle. History of variational principles in physics A variational principle in physics is an alternative method for determining the state or dynamics of a physical system, by identifying it as an
Physics engine Physics engine A physics engine is computer software that provides an approximate simulation of certain physical systems, such as rigid body dynamics (including collision detection), soft body dynamics, and fluid dynamics, of use in the domains of computer graphics, video games and film. Their main uses are in video games (typically as middleware), in which case the simulations are in real-time. The term is sometimes used more generally to describe any software system for simulating physical phenomena, such as high-performance scientific simulation. There are generally two classes of physics engines: real-time and high-precision. High-precision physics engines require more processing power