物理学报Issue(4)：312-318,7.DOI:10.7498/aps.62.044601
精确Cosserat弹性杆动力学的分析力学方法
Methods of analytical mechanics for exact Cosserat elastic rod dynamics∗
摘要
Abstract
Thin elastic rod mechanics with background of a kind of single molecule such as DNA and other engineering object has entered into a new developing stage. In this paper the vector method of exact Cosserat elastic rod dynamics is transformed into the form of analytical mechanics with the arc length and time as its independent variables, whose aims are to find new tools for studying rod mechanics and to develop the area of applications of classical analytical mechanics. Based on the plane cross-section assumption, a cross-section of the rod is taken as an object. Basic formulas on deformation and motion of the section are given. After defining virtual displacement of a cross-section and its equivalent variation rule, a differential variational principle such as d’Alembert-Lagrange one is established, from which dynamical equations of thin elastic rod are expressed as Lagrange equations or Nielsen equations under the condition of linear elasticity of the rod. For the rod statics when there exist conserved quantities, Lagrange equation which makes use of these quantities is derived and its first integral is discussed. Finally integral variational principle is derived from differential one, and expressed as Hamilton principle under the condition of linear elasticity. Hamilton canonical equations in phase space with 3×6 dimensions are also derived. All of the results have formed the method of analytical mechanics of dynamics of an exact Cosserat elastic rod, so that the further problems such as symmetry and conserved quantities, and numerical simulation of the rod dynamics may be further studied.关键词
精确Cosserat弹性杆/分析动力学方法/变分原理/Lagrange方程Key words
an exact Cosserat elastic rod/analytical dynamics/variational principle/Lagrange equation Hamilton principle引用本文复制引用
薛纭,翁德玮,陈立群..精确Cosserat弹性杆动力学的分析力学方法[J].物理学报,2013,(4):312-318,7.基金项目
国家自然科学基金(批准号:51276192)资助的课题 （批准号:51276192）
