# principle of least action

Also found in: Dictionary, Wikipedia.

## 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 ?
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.
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).
After applying the principle of least action to this Lagrangian we obtain equations for the gravitational and electromagnetic fields (76), the equation of substance motion (80), and the equation for the metric (81) and the relation for the cosmological constant (82).

Site: Follow: Share:
Open / Close