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Noether’s theorem in peridynamics
Mathematics and Mechanics of Solids, 2018By introducing a new nonlocal argument, the Lagrangian formulation of peridynamics is investigated. The peridynamic Euler–Lagrange equation is derived from Hamilton’s principle, and Noether’s theorem is extended into peridynamics. With the help of the peridynamic Noether’s theorem, the conservation laws relevant to energy, linear momentum, angular ...
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On a geometric generalization of the noether theorem
1986Task of this paper is to compare some geometric approaches to obtain conservation laws associated to partial differential equations. More precisely we intend to consider the methods developed by A. Prastaro and A. M. Vinogradov.
MARINO V, PRASTARO, Agostino
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2009
A central recurring theme in mathematical physics is the connection between symmetries and conservation laws, in particular the connection between the symmetries of Euclidean space under rotation and translation and the conservation laws for linear and angular momentum.
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A central recurring theme in mathematical physics is the connection between symmetries and conservation laws, in particular the connection between the symmetries of Euclidean space under rotation and translation and the conservation laws for linear and angular momentum.
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Noether's Theorem in Symplectic Bundles
International Journal of Theoretical Physics, 2000The authors first discuss different kinds of symplectic bundles and their potential use in general relativity. They argue that the concept of symplectic fibration (which generalizes the notion of symplectic vector space) is somewhat too general for their purposes, and propose instead to work on seeded fibre bundles (SFB), as introduced by \textit{V ...
Liern, V., Moreno, J. M., Olivert, J.
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2019
The significance of Noether’s theorem in gauge theory is given. Applications in physics are illustrated by a few examples. To apply Noether’s theorem, the Lagrangian mechanics has to be used.
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The significance of Noether’s theorem in gauge theory is given. Applications in physics are illustrated by a few examples. To apply Noether’s theorem, the Lagrangian mechanics has to be used.
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On the Lasker-Noether Decomposition Theorem
American Journal of Mathematics, 1984This is a paper on Noetherian rings from a constructive point of view. It is a natural continuation of a previous paper by the author [Trans. Am. Math. Soc. 197, 273-313 (1974; Zbl 0356.13007)] where it was shown how to construct a primary decomposition and to find the associated prime ideals of a given ideal in a polynomial ring over a field.
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2011
A major contribution to the development of the physics of fundamental interactions, in fact for the whole physics, was the theorem developed by Emmy Noether in 1918 [10, 105, 106], showing how to construct the observables of a theory, given its Lagrangian and Lie symmetry groups.
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A major contribution to the development of the physics of fundamental interactions, in fact for the whole physics, was the theorem developed by Emmy Noether in 1918 [10, 105, 106], showing how to construct the observables of a theory, given its Lagrangian and Lie symmetry groups.
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New Approach to the Noether Theorems
Journal of Mathematical Physics, 1971The Noether theorems were derived by Noether for n-dimensional Euclidean spaces, but they have been used by many writers in relativistic theories where the geometry is not Euclidean. We give a derivation of the Noether theorems, assuming only a Riemannian space and following the method used by Noether as closely as possible.
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Hamilton’s Principle and Noether’s Theorem
2005Abstract This chapter presents extended forms of Hamilton’s principle and the phase space Hamilton’s principle based on the extended Lagrangian and Hamiltonian methods developed earlier. It also discusses Noether’s theorem, a method for using symmetries of the extended Lagrangian to identify quantities that are conserved during the ...
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