Discrete variational principle and the first integrals of the conservative holonomic systems in event space

2005 ◽  
Vol 14 (5) ◽  
pp. 888-892 ◽  
Author(s):  
Zhang Hong-Bin ◽  
Chen Li-Qun ◽  
Liu Rong-Wan
Keyword(s):  
Variational Principle ◽  
First Integrals ◽  
Event Space ◽  
Holonomic Systems

Variational principle and dynamical equations of discrete nonconservative holonomic systems

2006 ◽  
Vol 15 (2) ◽  
pp. 249-252 ◽  
Author(s):  
Liu Rong-Wan ◽  
Zhang Hong-Bin ◽  
Chen Li-Qun
Keyword(s):  
Variational Principle ◽  
Dynamical Equations ◽  
Holonomic Systems

scholarly journals Optimal Shape and First Integrals for Inverted Compressed Column

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 334
Author(s):  
Enes Kacapor ◽  
Teodor M. Atanackovic ◽  
Cemal Dolicanin
Keyword(s):  
Variational Principle ◽  
First Integrals ◽  
Arbitrary Cross Section ◽  
Optimal Shape ◽  
Equilibrium Equations ◽  
Concentrated Force ◽  
Cross Sectional ◽  
Nonlinear Equilibrium ◽  
Elastic Column ◽  
Special Case

We study optimal shape of an inverted elastic column with concentrated force at the end and in the gravitational field. We generalize earlier results on this problem in two directions. First we prove a theorem on the bifurcation of nonlinear equilibrium equations for arbitrary cross-section column. Secondly we determine the cross-sectional area for the compressed column in the optimal way. Variational principle is constructed for the equations determining the optimal shape and two new first integrals are constructed that are used to check numerical integration. Next, we apply the Noether’s theorem and determine transformation groups that leave variational principle Gauge invariant. The classical Lagrange problem follows as a special case. Several numerical examples are presented.

Rotating fluid masses in general relativity. II

1966 ◽  
Vol 62 (3) ◽  
pp. 495-501 ◽  
Author(s):  
R. H. Boyer
Keyword(s):  
General Relativity ◽  
Variational Principle ◽  
First Integrals ◽  
Constant Angular Velocity ◽  
Hydrodynamic Equations ◽  
Rotating Fluid ◽  
Axially Symmetric ◽  
Field Equations ◽  
Full Field ◽  
Specific Entropy

AbstractWe describe some properties of a stationary, isolated, axially symmetric, rotating body of perfect fluid, according to general relativity. We first specialize to the case of constant specific entropy and constant angular velocity. The latter condition is equivalent to rigidity in the Born sense; both conditions are consequences of a simple variational principle. The hydrodynamic equations can then be integrated completely. Analogous first integrals are given also for the case of differential rotation. No use is made of the full field equations.

scholarly journals First integrals of holonomic systems without Noether symmetries

2020 ◽  
Vol 61 (12) ◽  
pp. 122701
Author(s):  
Michael Tsamparlis ◽  
Antonios Mitsopoulos
Keyword(s):  
First Integrals ◽  
Noether Symmetries ◽  
Holonomic Systems

First Integrals of Discrete System Based on the Principle of Jourdain

2012 ◽  
Vol 479-481 ◽  
pp. 711-714 ◽  
Author(s):  
Ning Zhang ◽  
Gang Ling Zhao
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Variational Principle ◽  
Discrete System ◽  
Discrete Dynamical System ◽  
Variational Formula ◽  
Discrete Analog ◽  
Discrete Dynamical Systems ◽  
First Integrals ◽  
Discrete Transformation

In this paper, we investigate first integrals of discrete dynamical systems with the variational principle of Jourdain. The operators of discrete transformation are introduced for the system. Based on the Jourdainian generalized variational formula, we derive the discrete analog of Noether-type identity, and then we obtain the first integrals of discrete dynamical system. We discuss an example to illustrate these results.

scholarly journals Emmy Noether and Linear Evolution Equations

10.14311/1811 ◽  
2013 ◽  
Vol 53 (3) ◽  
Author(s):  
P. G. L. Leach
Keyword(s):  
Variational Principle ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Evolution Equations ◽  
First Integrals ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Linear Evolution ◽  
Action Integral ◽  
Linear Evolution Equations

Noether’s Theorem relates the Action Integral of a Lagrangian with symmetries which leave it invariant and the first integrals consequent upon the variational principle and the existence of the symmetries. These each have an equivalent in the Schrödinger Equation corresponding to the Lagrangian and by extension to linear evolution equations in general. The implications of these connections are investigated.

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