Two forms of the discrete equations and the Noether theorems for nonautonomous Birkhoffian systems

2021 ◽  
Vol 11 (4) ◽  
Author(s):  
Lili Xia ◽  
Xinsheng Ge ◽  
Liqun Chen
Keyword(s):  
Discrete Equations

scholarly journals Stability of Nonlinear Autonomous Quadratic Discrete Systems in the Critical Case

2010 ◽  
Vol 2010 ◽  
pp. 1-23 ◽  
Author(s):  
Josef Diblík ◽  
Denys Ya. Khusainov ◽  
Irina V. Grytsay ◽  
Zdenĕk Šmarda
Keyword(s):  
Lyapunov Functions ◽  
Critical Case ◽  
Autonomous Systems ◽  
Discrete Systems ◽  
Simple Eigenvalue ◽  
Discrete Equations ◽  
The Matrix ◽  
The Stability ◽  
Important Characterization

Many processes are mathematically simulated by systems of discrete equations with quadratic right-hand sides. Their stability is thought of as a very important characterization of the process. In this paper, the method of Lyapunov functions is used to derive classes of stable quadratic discrete autonomous systems in a critical case in the presence of a simple eigenvalueλ=1of the matrix of linear terms. In addition to the stability investigation, we also estimate stability domains.

Comments on the Use of Lotka's Discrete Equations

Oikos ◽  
1991 ◽  
Vol 62 (1) ◽  
pp. 118 ◽  
Author(s):  
Bertram G. Murray
Keyword(s):  
Discrete Equations

Finite Volume Method for Computation of Water Hammer in Conical Tubes

2014 ◽  
Vol 563 ◽  
pp. 266-269
Author(s):  
Xiu Long Zhao ◽  
Jian Zhang ◽  
De Shuang Yu
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
High Accuracy ◽  
Water Hammer ◽  
Simple Derivation ◽  
Conical Tube ◽  
Discrete Equations ◽  
Volume Method ◽  
Approximate Treatment ◽  
Derivation Process

The most traditional way to calculate water hammer in the conical tube is using some small discrete equivalent uniform tubes to replace it. this approximate treatment can not show the much accurate results of the conical tube,but also not reflect the actual physical discontinuities of the system.This paper use finite volume method to integrate water hammer equations in conical tubes on spatial and temporal scales.Compare the results of FVM discrete equations with MOC. Conclusion shows that: the new discrete equations not only has high accuracy and stability in the calculation of water hammer in conical tubes,but also has a simple derivation process and clear physical meanings.This method provides a new way of thinking in water hammer calculation of conical tubes.

A General Version of the Retract Method for Discrete Equations

2006 ◽  
Vol 23 (2) ◽  
pp. 341-348 ◽  
Author(s):  
Josef Diblík ◽  
Irena Růžičková ◽  
Miroslava Růžičková
Keyword(s):  
General Version ◽  
Discrete Equations

Targeted Energy Transfer to a Rotary Nonlinear Energy Sink

2010 ◽  
Author(s):  
Sean A. Hubbard ◽  
D. Michael McFarland ◽  
Alexander F. Vakakis ◽  
Lawrence A. Bergman
Keyword(s):  
Finite Element ◽  
Energy Transfer ◽  
Finite Element Model ◽  
Nonlinear Energy Sink ◽  
Element Model ◽  
Targeted Energy Transfer ◽  
Discrete Equations ◽  
Resonant Interactions ◽  
Energy Sink ◽  
Nonlinear Energy

We study computationally the passive, nonlinear targeted energy transfers induced by resonant interactions between a single-degree-of-freedom nonlinear energy sink and a uniform-plate model of a flexible, swept aircraft wing. We show that the nonlinear energy sink can be designed to quickly and efficiently absorb energy from one or more wing modes in a completely passive manner. Results indicate that it is feasible to use such a device to suppress or prevent aeroelastic instabilities like limit-cycle oscillations. The design of a compact nonlinear energy sink is introduced and the parameters of the device are examined. Simulations performed using a finite-element model of the wing coupled to discrete equations governing the energy sink indicate that targeted energy transfer is achievable, resulting, for example, in a rapid and significant reduction in the second bending mode response of the wing. Finally, the finite element model is used to simulate the effects of increased nonlinear energy sink stiffness, and to show the conditions under which the nonlinear energy sink will resonantly interact with higher-frequency wing modes.

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