BOLT
发表于 2025-3-28 14:37:52
,Euler-Poincaré Equation Approach,wed that the equations for ideal, incompressible fluid dynamics could be derived from a variational principle in which the Lagrangian consists of the fluid kinetic energy, subject to an infinite Lie group (pseudo-Lie group) constraint, associated with the Lagrangian map (the constraint is that the L
Concerto
发表于 2025-3-28 19:20:02
Hamiltonian Approach,range multipliers to enforce the constraints of mass conservation; the entropy advection equation; Faraday’s equation and the so-called Lin constraint describing in part, the vorticity of the flow (i.e. Kelvin’s theorem). This leads to Hamilton’s canonical equations in terms of Clebsch potentials. T
江湖郎中
发表于 2025-3-29 02:49:01
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Morose
发表于 2025-3-29 04:16:58
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MEN
发表于 2025-3-29 09:14:06
MHD Stability,bria was investigated in the seminal paper by Bernstein et al. (.) who derived sufficient conditions for magneto-static equilibria, based on the so-called energy principle. A sufficient, but not necessary condition for magnetostatic equilibria is that the potential energy functional .(., .) satisfie
不知疲倦
发表于 2025-3-29 13:01:54
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熟练
发表于 2025-3-29 15:49:27
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Conscientious
发表于 2025-3-29 23:41:52
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Offbeat
发表于 2025-3-30 03:36:14
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讨好女人
发表于 2025-3-30 07:47:53
Introduction,for systems of differential equations governed by an action principle. Noether’s theorem applies to systems of Euler-Lagrange equations that are in Kovalevskaya form (e.g Olver (1993)). For other Euler-Lagrange systems, each nontrivial variational symmetry leads to a conservation law, but there is no guarantee that it is non-trivial.