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131.
该文研究一类五次多项式微分系统在高次奇点与无穷远点的极限环分支问题. 该系统的原点是高次奇点, 赤道环上没有实奇点. 首先推导出计算高次奇点与无穷远点奇点量的代数递推公式,并用之计算系统原点、无穷远点的奇点量,然后分别讨论了系统原点、无穷远点中心判据. 给出了多项式系统在高次奇点分支出5个极限环同时在无穷远点分支出2个极限环的实例. 这是首次在同步扰动的条件下讨论高次奇点与无穷远点分支出极限环的问题. 相似文献
132.
Based on the total time
derivative along the trajectory of the system
the definition and the criterion for a unified symmetry of nonholonomic
mechanical system with variable mass are presented in this paper. A new
conserved quantity, as
well as the Noether conserved quantity and the Hojman conserved quantity,
deduced from the unified symmetry, are also obtained. An example is given to
illustrate the application of the results. 相似文献
133.
The Lagrangian and the Lie symmetries of charged particle motion in homogeneous electromagnetic field 下载免费PDF全文
In this paper, a constant of motion of charged particle motion in
homogeneous electromagnetic field is derived from Newton's equations and the
characteristics of partial differential equation, the related
Lagrangian is also given by means of the obtained constant of motion. By
discussing the Lie symmetry for this classical system, this paper
obtains the general
expression of the conserved quantity. It is shown that the conserved
quantity is the same as the constant of motion in essence. 相似文献
134.
The Mei symmetry of Tzénoff equations under the infinitesimal transformations of groups is studied in this paper. The definition and the criterion equations of the symmetry are given. If the symmetry is a Noether symmetry, then the Noether conserved quantity of the Tzénoff equations can be obtained by the Mei symmetry. 相似文献
135.
XIA Li-Li LI Yuan-Cheng HOU Qi-Bao WANG Jing 《理论物理通讯》2006,46(4):683-686
Based on the total time derivative along the trajectory of the system, the unified symmetry of nonholonomic mechanical system with non-Chetaev's type constraints is studied. The definition and criterion of the unified symmetry of nonholonomic mechanical systems with non-Ohetaev's type constraints are given. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symmetry, is obtained. Two examples are given to illustrate the application of the results. 相似文献
136.
This paper discusses the conformal invariance by infinitesimal
transformations of canonical Hamilton systems. The necessary and
sufficient conditions of conformal invariance being Lie symmetrical
simultaneously by the action of infinitesimal transformations are
given. The determining equations of the conformal invariance are
gained. Then the Hojman conserved quantities of conformal invariance
by special infinitesimal transformations are obtained. Finally an
illustrative example is given to verify the results. 相似文献
137.
In this paper, two types of new conserved quantities directly deduced by Mei symmetry in phase space are studied. The conditions under which Mei symmetry can directly lead to the two types of new conserved quantities and the forms of the two types of new conserved quantities are given. An example is given to illustrate the application of the results. 相似文献
138.
In this paper, we study the Noether-form invariance of nonholonomic mechanical controllable systems in phase space. Equations of motion of the controllable mechanical systems in
phase space are presented. The definition and the criterion for
this system are presented. A new conserved quantity and the
Noether conserved quantity deduced from the Noether-form invariance are obtained. An example is given to illustrate the application of the results. 相似文献
139.
In this paper, the form invariance and the Lie symmetry of Lagrange's equations for nonconservative system in generalized classical mechanics under the infinitesimal transformations of group are studied, and the Noether's conserved quantity, the new form conserved quantity, and the Hojman's conserved quantity of system are derived from them. Finally, an example is given to illustrate the application of the result. 相似文献
140.
A series of non-Noether conservative quantities and Mei symmetries of nonconservative systems 下载免费PDF全文
In this paper Mei symmetry is introduced for a nonconservative system. The necessary and
sufficient condition for a Mei symmetry to be also a Lie symmetry is
derived. It is proved that the Mei symmetry leads to a non-Noether
conservative quantity via a Lie symmetry, and deduces a Lutzky conservative
quantity via a Lie point symmetry. 相似文献