Lagrangian function

/leuh grayn"jee euhn/, Physics.See kinetic potential.[190005; named after J. L. LAGRANGE; see IAN]
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▪ physicsalso called Lagrangianquantity that characterizes the state of a physical system. In mechanics, the Lagrangian function is just the kinetic energy (energy of motion) minus the potential energy (energy of position).One may think of a physical system, changing as time goes on from one state or configuration to another, as progressing along a particular evolutionary path, and ask, from this point of view, why it selects that particular path out of all the paths imaginable. The answer is that the physical system sums the values of its Lagrangian function for all the points along each imaginable path and then selects that path with the smallest result. This answer suggests that the Lagrangian function measures something analogous to increments of distance, in which case one may say, in an abstract way, that physical systems always take the shortest paths.In the special case of a ray of light, the path of system configurations is just the ordinary path of the light through space, and the Lagrangian function reduces simply to a measure of the passage of time. The particular curved path that a light ray takes through a refracting lens is therefore just the one that takes the least time.The principle is, however, much more general than that, and it is a remarkable discovery that it seems to describe all phenomena equally well, including, for example, the travel of a rocket to the moon, and the likelihood that colliding subatomic particles will scatter each other in selected directions.* * *
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Lagrangian function — Lagranžo funkcija statusas T sritis fizika atitikmenys: angl. Lagrange function; Lagrangian function vok. Lagrange Funktion, f; Lagrangesche Funktion, f rus. лагранжева функция, f; функция Лагранжа, f pranc. fonction de Lagrange, f; fonction… … Fizikos terminų žodynas
lagrangian function — ləˈgranjēən noun Usage: usually capitalized L Etymology: Joseph L. Lagrange died 1813 Italian born geometer and astronomer in France + English ian : kinetic potential * * * /leuh grayn jee euhn/, Physics. See kinetic potential. [1900 05; name … Useful english dictionary
Lagrangian function — noun see kinetic potential * * * /leuh grayn jee euhn/, Physics. See kinetic potential. [1900 05; named after J. L. LAGRANGE; see IAN] * * * Lagrangian function, Physics. a function equal to the difference between the total kinetic energy and the … Useful english dictionary
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