Conservation laws of nonconservative nonholonomic system based on Herglotz variational problem

2019 ◽  
Vol 383 (8) ◽  
pp. 691-696 ◽  
Author(s):  
Yi Zhang ◽  
Xue Tian
Keyword(s):  
Conservation Laws ◽  
Variational Problem ◽  
Nonholonomic System

Conservation Laws in Circuit Theory

1980 ◽  
Vol 17 (4) ◽  
pp. 349-354
Author(s):  
J. David Logan
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Conservation Laws ◽  
Variational Problem ◽  
Electrical Engineering ◽  
Circuit Theory ◽  
First Integrals ◽  
Second Order Differential Equations ◽  
Engineering Problems ◽  
The Given

This article presents a method for determining first integrals for nonlinear second-order differential equations arising in electrical engineering problems. It is based on finding a set of transformations under which the variational problem associated with the given differential equation is invariant. An example involving a simple R-C-L circuit is presented.

scholarly journals Extensions of Noether's Second Theorem: from continuous to discrete systems

2011 ◽  
Vol 467 (2135) ◽  
pp. 3206-3221 ◽  
Author(s):  
Peter E. Hydon ◽  
Elizabeth L. Mansfield
Keyword(s):  
Finite Difference ◽  
Conservation Laws ◽  
Variational Problem ◽  
Discrete Systems ◽  
Lagrange Equations ◽  
Difference Systems

A simple local proof of Noether's Second Theorem is given. This proof immediately leads to a generalization of the theorem, yielding conservation laws and/or explicit relationships between the Euler–Lagrange equations of any variational problem whose symmetries depend on a set of free or partly constrained functions. Our approach extends further to deal with finite-difference systems. The results are easy to apply; several well-known continuous and discrete systems are used as illustrations.

Bosonic Symmetries, Solutions, and Conservation Laws for the Dirac Equation with Nonzero Mass

2013 ◽  
Vol 58 (6) ◽  
pp. 523-533 ◽  
Author(s):  
V.M. Simulik ◽  
◽  
I.Yu. Krivsky ◽  
I.L. Lamer ◽  
◽  
...  
Keyword(s):  
Dirac Equation ◽  
Conservation Laws

Conserved Quantities for the General Linear Heat Equation

2016 ◽  
pp. 4437-4439
Author(s):  
Adil Jhangeer ◽  
Fahad Al-Mufadi
Keyword(s):  
Evolution Equation ◽  
Heat Equation ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Lagrangian Approach ◽  
General Linear ◽  
Conserved Quantities ◽  
Linear Heat ◽  
The Family ◽  
Partial Lagrangian

In this paper, conserved quantities are computed for a class of evolution equation by using the partial Noether approach [2]. The partial Lagrangian approach is applied to the considered equation, infinite many conservation laws are obtained depending on the coefficients of equation for each n. These results give potential systems for the family of considered equation, which are further helpful to compute the exact solutions.

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