principle of least action


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principle of least action

[′prin·sə·pəl əv ‚lēst ′ak·shən]
(mechanics)
The principle that, for a system whose total mechanical energy is conserved, the trajectory of the system in configuration space is that path which makes the value of the action stationary relative to nearby paths between the same configurations and for which the energy has the same constant value. Also known as least-action principle.
References in periodicals archive ?
According to our previous papers, the Principle of Least Action explains the mechanism of increase of organization through quantity accumulation and constraint and curvature minimization with an attractor, the least average sum of actions of all elements and for all motions.
Thus, the observation by Moore is explained here as a part of this system of interfunctions driven by the Principle of Least Action. The visible oscillations of the data around the exponential and power-law fits (see Figures 2 and 3), which are their homeostatic values, can help explain the multiple logistic nature of technology substitution S-curves, by the negative feedback between the homeostatic values of the interfunctions, and the actual deviations of the data from them.
Chatterjee, "Principle of least action and convergence of systems towards state of closure," International Journal of Physical Research, vol.
In this section we shall write down known relations for the Lagrange function and the principle of least action for the covariant theory of gravitation (CTG).
We shall remind that the principle of least action is usually applied to conservative systems for which precise potential functions are given, from which acting forces can be found.
Describing the principle of least action, we recorded the Lagrange function in the general form: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where the quantities X=dx/dt, y= dy/dt, z=dz/dt are the components of 3-vector of coordinate velocity [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] of the substance unit motion.
With the vanishing of the variation in time, as it is required for the Lagrange function in the principle of least action, for the variation of the Hamiltonian we have:
By the principle of least action, the variation of the action must be equal to zero: [delta]S = [integral]L dt = [delta][S.sub.1] +[delta][S.sub.2] = 0.
From the stated above it follows that the action is not only a function by which from the principle of least action the equations of motion are obtained, through the Legendre transformation the Hamiltonian, or the Hamilton-Jacobi equations are defined.
Based on the principle of least action and Euler-Lagrange equations, we presented in (17) the relativistic equation of motion of a substance unit in fundamental fields (for motion along the axis OX of the Cartesian reference frame).

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