Construction of a new Lyapunov function for a dissipative gyroscopic system using the residual energy function

CİVELEK Cem; CİHANBEĞENDİ Özge

doi:10.1631/FITEE.1900014

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Construction of a new Lyapunov function for a dissipative gyroscopic system using the residual energy function

Regular Papers | Updated：2022-05-19

- Construction of a new Lyapunov function for a dissipative gyroscopic system using the residual energy function
- 耗散陀螺系统的李雅普诺夫函数构造：剩余能量函数方法
- Frontiers of Information Technology & Electronic Engineering Vol. 21, Issue 4, Pages: 629-634(2020)
- Affiliations：
  
  Faculty of Engineering, Department of Electrical and Electronics Engineering, Ege University, Bornova-İzmir 35100, Turkey
  Faculty of Engineering, Department of Electrical and Electronics Engineering, Dokuz Eylul University, Buca-İzmir 35160, Turkey
- Author bio：
  
  Cem CİVELEK, E-mail: cem.civelek@ege.edu.tr
  [ "Özge CİHANBEĞENDİ, E-mail: ozge.sahin@deu.edu.tr" ]
- Funds：
- DOI：10.1631/FITEE.1900014
  CLC： O313
- Published：2020-04，
  
  Received：10 January 2019，
  
  Revised：06 March 2020，
- Accepted：
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CİVELEK CEM, CİHANBEĞENDİ ÖZGE. Construction of a new Lyapunov function for a dissipative gyroscopic system using the residual energy function. [J]. Frontiers of information technology & electronic engineering, 2020, 21(4): 629-634.
DOI：

CİVELEK CEM, CİHANBEĞENDİ ÖZGE. Construction of a new Lyapunov function for a dissipative gyroscopic system using the residual energy function. [J]. Frontiers of information technology & electronic engineering, 2020, 21(4): 629-634. DOI： 10.1631/FITEE.1900014.

摘要

在自由度为4、张量有逆变（右上标）和协变（右下标）形式的耗散陀螺系统中，使用二阶线性微分方程建立拉格朗日耗散模型，即{L

D}模型。通过系统的{L

D}模型确定广义元素。满足勒让德变换先决条件时，可得哈密顿量。剩余能量函数（REF）由哈密顿量及损耗或耗散能量（为负）之和组成，将其作为李雅普诺夫函数，可通过李雅普诺夫第二方法作稳定性分析，并从数学上推导出稳定性条件。

Abstract

In a dissipative gyroscopic system with four degrees of freedom and tensorial variables in contravariant (right upper index) and covariant (right lower index) forms

a Lagrangian-dissipative model

i.e.

{

}-model

is obtained using second-order linear differential equations. The generalized elements are determined using the {

}-model of the system. When the prerequisite of a Legendre transform is fulfilled

the Hamiltonian is found. The Lyapunov function is obtained as a residual energy function (REF). The REF consists of the sum of Hamiltonian and losses or dissipative energies (which are negative)

and can be used for stability by Lyapunov's second method. Stability conditions are mathematically proven.

关键词

李雅普诺夫函数剩余能量函数耗散陀螺系统稳定性

Keywords

Lyapunov functionResidual energy functionStability of dissipative gyroscopic system

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