The reducibility of the equations of free motion of a complex mechanical system |
| |
| Institution: | 1. Ophtalmology departement, CHU de Rennes, 2, rue Henri-Le-Guilloux, 35000 Rennes, France;2. Ophtalmology departement, French Society of ophthalmologic telemedicine, CHU de Rennes, 2, rue Henri-Le-Guilloux, 35000 Rennes, France;1. Key Laboratory of Solidification Control and Digital Preparation Technology (Liaoning Province), School of Materials Science and Engineering, Dalian University of Technology, Dalian 116024, China;2. Ningbo Institute of Dalian University of Technology, Ningbo 315016, China;3. Key Laboratory of Lightweight Structural Materials (Liaoning Province), School of Materials Science and Engineering, Northeastern University, Shenyang 110819, China;4. Engineering Institute, Bohai University, Jinzhou 121013, China;1. Federal University of ABC, Center of Mathematics, Santo André, 09210-580, Brazil;2. Federal University of Alfenas, Physics Department: Institute of Exact Sciences, Alfenas 37133-840, Brazil;1. Martin-Luther-University Halle-Wittenberg, Center of Engineering Sciences, 06099 Halle/Saale, Germany;2. Pennsylvania State University, School of Engineering, 4701 College Drive, Erie, PA 16563, USA;3. University of Rostock, Institute of Physics, Wismarsche Str. 43–45, 18051 Rostock, Germany;1. School of Chemical Engineering, University of Birmingham, Edgbaston, B15 2TT, United Kingdom;2. School of Chemistry, University of Keele, Staffordshire ST5 5BG, United Kingdom;3. Diamond Light Source, Harwell Science and Innovation Campus, Didcot OX11 0DE, United Kingdom;4. RISE Research Institutes of Sweden, Surfaces, Processes, and Formulation, SE-114 86 Stockholm, Sweden;5. Procter and Gamble Brussels Innovation Center, Temselaan 100, 1853 Strombeek Bever, Belgium;6. School of Chemistry, University of Birmingham, Edgbaston, B15 2TT, United Kingdom;7. Department of Chemical and Environmental Engineering, University of Nottingham, Nottingham NG7 2RD, United Kingdom |
| |
| Abstract: | A mechanical system consists of an unchangeable rigid body (a carrier) and a subsystem whose configuration and composition may vary with time (the motion of its elements relative to the carrier is given). The free motion of the system in a uniform gravitational field is investigated, on the assumption that there is no dynamic symmetry. Necessary and sufficient conditions are derived for the existence of two integrals, each quadratic in the components of the absolute angular velocity of the carrier. Lt is shown that the initial dynamical system can be reduced to an autonomous gyrostat system if and only if the motion has these two quadratic integrals; the explicit form of a linear transformation to the autonomous system is indicated. The explicit form of the integrals and conditions for their existence are obtained. Examples of motion with two quadratic integrals are considered. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
