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
Interaction technique line and direct manipulation user interfaces. While interaction techniques are typically technology-, platform-, and/or implementation-dependent (see #level of granularity above), human-computer or human-information interactions can be characterized at higher levels of abstraction that are independent of particular technologies and platforms. At such levels of abstraction, the concern is not precisely how an interaction is performed; rather, the concern is a conceptual characterization of what the interaction is, and what the general utility of the interaction is for the user(s). Thus, any single interaction pattern may be instantiated by any number of interaction techniques, on any number of different technologies and