Conservation Laws for a Dynamical System in Group Variables

1982 ◽  
Vol 62 (9) ◽  
pp. 441-446
Author(s):  
M. Hussain
Keyword(s):  
Dynamical System ◽  
Conservation Laws

Conservation laws

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Dynamical System ◽  
Angular Momentum ◽  
Conservation Laws ◽  
Total Energy ◽  
Superposition Principle ◽  
Momentum Conservation ◽  
Conserved Quantities ◽  
Angular Momentum Conservation ◽  
Third Law ◽  
The Law

This chapter defines the conserved quantities associated with an isolated dynamical system, that is, the quantities which remain constant during the motion of the system. The law of momentum conservation follows directly from Newton’s third law. The superposition principle for forces allows Newton’s law of motion for a body Pa acted on by other bodies Pa′ in an inertial Cartesian frame S. The law of angular momentum conservation holds if the forces acting on the elements of the system depend only on the separation of the elements. Finally, the conservation of total energy requires in addition that the forces be derivable from a potential.

scholarly journals Conservation laws in a first-order dynamical system of vortices

Nonlinearity ◽  
1999 ◽  
Vol 12 (4) ◽  
pp. 851-865 ◽  
Author(s):  
N S Manton ◽  
S M Nasir
Keyword(s):  
Dynamical System ◽  
Conservation Laws ◽  
First Order

scholarly journals On Algorithm of Integrability Classification of the Nonlinear Dynamical Systems via Computer Algebra Methods

2021 ◽  
pp. 7-12
Author(s):  
Bohdan Fil ◽  
Yaroslav Pelekh ◽  
Myroslava Vovk ◽  
Halyna Beregova ◽  
Tatiana Magerovska ◽  
...  
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Conservation Laws ◽  
Computer Algebra ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Nonlinear Dynamical ◽  
Wolfram Mathematica ◽  
De Vries

There is developed an algorithm to classify integrable nonlinear dynamical systems via Wolfram Mathematica. The hierarchy of conservation laws for the nonlinear dynamical system can be cal-culated by this algorithm. There are demonstrated some modifications of nonlinear Korteweg-de Vries equations integrated by inverse scatering method.

scholarly journals A Constructive Method for Computing Generalized Manley-Rowe Constants of Motion

2013 ◽  
Vol 14 (4) ◽  
pp. 1094-1102
Author(s):  
Elena Kartashova ◽  
Loredana Tec
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Conservation Laws ◽  
Time Evolution ◽  
Numerical Study ◽  
Constructive Method ◽  
Constants Of Motion

AbstractThe Manley-Rowe constants of motion (MRC) are conservation laws written out for a dynamical system describing the time evolution of the amplitudes in resonant triad. In this paper we extend the concept of MRC to resonance clusters of any form yielding generalized Manley-Rowe constants (gMRC) and give a constructive method how to compute them. We also give details of a Mathematica implementation of this method. While MRC provide integrability of the underlying dynamical system, gMRC generally do not but may be used for qualitative and numerical study of dynamical systems describing generic resonance clusters.

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