The stability and stabilization of the motion of non-conservative mechanical systems |
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| Authors: | SA Agafonov |
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| Institution: | 1. Center for General Education, National Formosa University, Huwei 632, Taiwan;2. Department of Mathematics, National Chung Cheng University, Chia-Yi 621, Taiwan;1. Department of Mathematics & Computing, Indian Institute of Technology Dhanbad, Dhanbad 826004, India;2. Department of Statistics, Pandit Deendayal Upadhyaya Adarsha Mahavidyalaya, Eraligool, Karimganj 788723, India;3. Division of Science and Technology, Beijing Normal University–Hong Kong Baptist University United International College, Zhuhai 519085, China;4. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt;1. Departamento de Matemáticas, Universidad Carlos III de Madrid, Avda. Universidad 30, 28911 Leganés, Spain;2. Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM and Departamento de Matemáticas, Universidad Carlos III de Madrid, Avda. Universidad 30, 28911 Leganés, Spain;3. Department of Mathematics, Western Michigan University, Kalamazoo, MI 49008, USA;1. Laboratory of Applied Mathematics, Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, I-38123 Trento, Italy;2. Physics Department, University of Notre Dame du Lac, 225 Nieuwland Science Hall, Notre Dame, IN 46556, USA |
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| Abstract: | Two stability problems are solved. In the first, the stability of mechanical systems, on which dissipative, gyroscopic, potential and positional non-conservative forces (systems of general form) act, is investigated. The stability is considered in the case when the potential energy has a maximum at equilibrium. The condition for asymptotic stability is obtained by constructing Lyapunov's function. In the second problem, the possibility of stabilizing a gyroscopic system with two degrees of freedom up to asymptotic stability using non-linear dissipative and positional non-conservative forces is investigated. Stability of the gyroscopic system is achieved by gyroscopic stabilization. The stability conditions are obtained in terms of the system parameters. Cases when the gyroscopic stabilization is disrupted by these non-linear forces are indicated. |
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