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Philippe Askenazy 《Journal of Mathematical Analysis and Applications》2003,282(2):603-613
This paper provides a new simple version of Noether's theorem. From symmetries of dynamic optimal programs, this theorem gives invariant quantities along optimal paths. It is suited to optimal control programs especially for economic models. Applications in growth economics are given. 相似文献
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Nail H. Ibragimov 《Journal of Mathematical Analysis and Applications》2006,318(2):742-757
Integrating factors and adjoint equations are determined for linear and non-linear differential equations of an arbitrary order. The new concept of an adjoint equation is used for construction of a Lagrangian for an arbitrary differential equation and for any system of differential equations where the number of equations is equal to the number of dependent variables. The method is illustrated by considering several equations traditionally regarded as equations without Lagrangians. Noether's theorem is applied to the Maxwell equations. 相似文献
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重建极性连续统理论的基本定律和原理(Ⅲ)--Noether定理 总被引:6,自引:6,他引:0
对现有的各种偶应力理论进行了认真的再研究,目的是要提出一个耦合型的Noether定理并由此重新建立偶应力弹性动力学的较为完整的守恒定律和相应的均衡方程.这里给出了新的各种守恒定律和均衡方程的具体形式,并建立起从给定的不变性要求所得到的这类守恒定律的确切属性.最后,由这里的结果自然地推导出各种特殊情形;并可自然地过渡到微极连续统的结果. 相似文献
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本文构造了力学系统相对运动的Lagrange函数,建立了非线性非完整非有势系统相对于非惯性系的Jourdain型变分原理,提出并证明了这类力学系统相对于非惯性系的广义Noether定理,研究了其守恒量. 相似文献
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Gastão S.F. Frederico 《Journal of Mathematical Analysis and Applications》2007,334(2):834-846
Fractional (or non-integer) differentiation is an important concept both from theoretical and applicational points of view. The study of problems of the calculus of variations with fractional derivatives is a rather recent subject, the main result being the fractional necessary optimality condition of Euler-Lagrange obtained in 2002. Here we use the notion of Euler-Lagrange fractional extremal to prove a Noether-type theorem. For that we propose a generalization of the classical concept of conservation law, introducing an appropriate fractional operator. 相似文献
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