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Constrained mechanical systems and gradient systems with strong Lyapunov functions
Affiliation:1. School of Physics and Electrical Information Science, Shangqiu Normal University, Shangqiu 476000, China;2. School of Aerospace, Beijing Institute of Technology, Beijing 100081, China;1. University of Sassari, Italy;2. University of Roma “La Sapienza”, Italy;3. Roma Tre University, Italy;4. MEMOCS, Italy;5. Warsaw University of Technology, Poland;6. Technische Universität Berlin, Germany;1. GRESPI/Thermomécanique, Université de Reims Champagne-Ardenne, Moulin de la Housse, BP 1039, 51687 Reims Cedex 2, France;2. Laboratoire d’Energétique Appliquée et de Pollution, Université Constantine 1, Constantine 25000, Algeria;3. Laboratoire de Mécanique, Physique et Modélisation Mathématique, Université de Médéa, 26000 Médéa, Algeria;4. Faculté des Hydrocarbures et Energies renouvelables et Sciences de la terre et de l’univers, Université Kasdi Merbah, 30000 Ouargla, Algeria;1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;2. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China;3. Department of Mechanics, Shanghai University, Shanghai 200444, China;1. Scuola di Scienze e Tecnologie, Sezione di Matematica, Università di Camerino, Italy;2. Departamento de Matemática, Universidade de São Paulo, Rua do Matão, 1010, 05508-090 São Paulo, SP, Brazil
Abstract:
The characteristics of stationary and non-stationary gradient systems with strong Lyapunov functions are studied. The conditions under which holonomic mechanical systems, generalized Birkhoff systems and generalized Hamilton systems can be considered as gradient systems are given. The characteristics of the gradient systems can be used to study the stability of the mechanical systems. Some examples are given to illustrate the application of the results.
Keywords:Constrained mechanical system  Gradient system  Stability  Strong Lyapunov function
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