According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for electroma...According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for electromagnetic elastodynamics can be established systematically. This new variational principles can fully characterize the initial-boundary-value problem of this dynamics. In this paper, the expression of the generalized principle of virtual work for electromagnetic dynamics is given. Based on this equation, it is possible not only to obtain the principle of virtual work in electromagnetic dynamics, but also to derive systematically the complementary functionals for eleven-field, nine-field and six-field unconventional Hamilton-type variational principles for electromagnetic elastodynamics, and the potential energy functionals for four-field and three-field ones by the generalized Legendre transformation given in this paper. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly.展开更多
According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the un-conventional Hamilton-type variational principles of holonomic...According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the un-conventional Hamilton-type variational principles of holonomic conservative system in analytical mechanics can be established systematically. This unconventional Hamilton-type variational principle can fully characterize the initial-value problem of analytical mechanics, so that it is an important innovation for the Hamilton-type variational principle. In this paper, an important integral relation is given, which can be considered as the expression of the generalized principle of virtual work for analytical mechanics in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work of holonomic conservative system in analytical mechanics, but also to derive systematically the complementary functionals for three-field and two-field unconventional variational principles, and the functional for the one-field one by the generalized Legendre transformation given in this paper. Further, with this new approach, the intrinsic relationship among various principles can be explained clearly. Meanwhile, the unconventional Hamilton-type variational principles of nonholonomic conservative system in analytical mechanics can also be established systematically in this paper.展开更多
基金the National Natural Science Foundation of China ( Grant No. 10172097) the Scientific Foundation of the Ministry of Education of China for Doctoral Program ( Grant No. 20030558025).
文摘According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for electromagnetic elastodynamics can be established systematically. This new variational principles can fully characterize the initial-boundary-value problem of this dynamics. In this paper, the expression of the generalized principle of virtual work for electromagnetic dynamics is given. Based on this equation, it is possible not only to obtain the principle of virtual work in electromagnetic dynamics, but also to derive systematically the complementary functionals for eleven-field, nine-field and six-field unconventional Hamilton-type variational principles for electromagnetic elastodynamics, and the potential energy functionals for four-field and three-field ones by the generalized Legendre transformation given in this paper. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly.
基金the National Natural Science Foundation of China(Grant Nos. 10172097 & 10272034)the Science Foundation for Doctoral Program of Ministry of Education of China (Grant No. 20030558025)
文摘According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the un-conventional Hamilton-type variational principles of holonomic conservative system in analytical mechanics can be established systematically. This unconventional Hamilton-type variational principle can fully characterize the initial-value problem of analytical mechanics, so that it is an important innovation for the Hamilton-type variational principle. In this paper, an important integral relation is given, which can be considered as the expression of the generalized principle of virtual work for analytical mechanics in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work of holonomic conservative system in analytical mechanics, but also to derive systematically the complementary functionals for three-field and two-field unconventional variational principles, and the functional for the one-field one by the generalized Legendre transformation given in this paper. Further, with this new approach, the intrinsic relationship among various principles can be explained clearly. Meanwhile, the unconventional Hamilton-type variational principles of nonholonomic conservative system in analytical mechanics can also be established systematically in this paper.
