Concept information
Terme préférentiel
Hamilton-Jacobi equation
Définition(s)
- In physics, the Hamilton–Jacobi equation, named after William Rowan Hamilton and Carl Gustav Jacob Jacobi, is an alternative formulation of classical mechanics, equivalent to other formulations such as Newton's laws of motion, Lagrangian mechanics and Hamiltonian mechanics. The Hamilton–Jacobi equation is particularly useful in identifying conserved quantities for mechanical systems, which may be possible even when the mechanical problem itself cannot be solved completely. The Hamilton–Jacobi equation is also the only formulation of mechanics in which the motion of a particle can be represented as a wave. In this sense, it fulfilled a long-held goal of theoretical physics (dating at least to Johann Bernoulli in the eighteenth century) of finding an analogy between the propagation of light and the motion of a particle. The wave equation followed by mechanical systems is similar to, but not identical with, Schrödinger's equation, as described below; for this reason, the Hamilton–Jacobi equation is considered the "closest approach" of classical mechanics to quantum mechanics. (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Hamilton%E2%80%93Jacobi_equation)
Concept(s) générique(s)
Traductions
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français
URI
http://data.loterre.fr/ark:/67375/MDL-QHC3T0GH-N
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