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Action principles are "integral" approaches rather than the "differential" approach of Newtonian mechanics.[2]: 162 The core ideas are based on energy, paths, an energy function called the Lagrangian along paths, and selection of a path according to the "action", a continuous sum or integral of the Lagrangian along the path.
The action is defined by an integral, and the classical equations of motion of a system can be derived by minimizing the value of that integral. The action principle provides deep insights into physics, and is an important concept in modern theoretical physics. Various action principles and related concepts are summarized below.
Hamilton's principle states that the true evolution q(t) of a system described by N generalized coordinates q = (q 1, q 2, ..., q N) between two specified states q 1 = q(t 1) and q 2 = q(t 2) at two specified times t 1 and t 2 is a stationary point (a point where the variation is zero) of the action functional [] = ((), ˙ (),) where (, ˙,) is the Lagrangian function for the system.
In Schwinger's approach, the action principle is targeted towards quantum mechanics. The action becomes a quantum action, i.e. an operator, . Although it is superficially different from the path integral formulation where the action is a classical function, the modern formulation of the two formalisms are identical. [4]
The variational principles approach to classical mechanics was developed parallelly with Newtonian mechanics. This article describes the historical development of such action principles and other variational methods applied in physics. See History of physics for an overview and Outline of the history of physics for related histories.
The terminology of action principles is inconsistent between sources. This issue is discussed in History_of_variational_principles_in_physics#action_principle_names. For the purpose of the merge, the important part is that "stationary action principle" is not universal or maybe even commonly used. The name "action principles" encompasses all of ...
Examples of principles are, entropy in a number of fields, least action in physics, those in descriptive comprehensive and fundamental law: doctrines or assumptions forming normative rules of conduct, separation of church and state in statecraft, the central dogma of molecular biology, fairness in ethics, etc.
Action Learning is ideologically a cycle of "doing" and "reflecting" stages. [5] In most forms of action learning, a coach is included and responsible for promoting and facilitating learning, as well as encouraging the team to be self-managing. The Action Learning process includes: An important and often complex problem; A diverse problem ...