Two kinds of generalized gradient systems are proposed and the characteristics of the two systems are studied. The conditions under which a holonomic mechanical system can be considered as one of the two generalized g...Two kinds of generalized gradient systems are proposed and the characteristics of the two systems are studied. The conditions under which a holonomic mechanical system can be considered as one of the two generalized gradient systems are obtained. The characteristics of the generalized gradient systems can be used to study the stability of the holonomic system. Some examples are given to illustrate the application of the results.展开更多
Two new types of conserved quantities directly deduced by Mei symmetry of holonomic mechanical system are studied. The definition and criterion of Mei symmetry for holonomic system are given. A coordination function i...Two new types of conserved quantities directly deduced by Mei symmetry of holonomic mechanical system are studied. The definition and criterion of Mei symmetry for holonomic system are given. A coordination function is introduced, the conditions under which the Mei symmetry can directly lead to the two types of conserved quantities and the forms of the two types of conserved quantities are obtained. An illustrative example is given. The result indicates that the coordination function can be selected properly according to the demand of the gauge function, thereby the gauge function can be found out more easily. Furthermore, since the choice of the coordination function has multiformity, much T more conserved quantity of Mei symmetry for holonomic mechanical system can be obtained.展开更多
Based on the concept of adiabatic invariant,the perturbation to the Lie symmetry and adiabatic invariantsfor general holonomic mechanical systems are studied.The exact invariants induced directly from the Lie symmetry...Based on the concept of adiabatic invariant,the perturbation to the Lie symmetry and adiabatic invariantsfor general holonomic mechanical systems are studied.The exact invariants induced directly from the Lie symmetryof the system without perturbation are given.The perturbation to the Lie symmetry is discussed and the adiabaticinvariants that have the different form from that in[Act.Phys.Sin.55(2006)3236(in Chinese)]of the perturbedsystem,are obtained.展开更多
This paper uses Poincare’s formalism to study . the integral invariants of aconservative holonomic dynamical system Introducing new parameters for theasynchronous variation, a generalization of the poincare and ...This paper uses Poincare’s formalism to study . the integral invariants of aconservative holonomic dynamical system Introducing new parameters for theasynchronous variation, a generalization of the poincare and Poincare-Cartan integralinvariants is presented.展开更多
In this paper we use Poincaré’s equations in group variables to de- scribe the motion of a holonomic mechanical system and to determine Jacobi's mul- tiplier for the equations of motion.
基金supported by the National Natural Science Foundation of China(Grant No.11272050)
文摘Two kinds of generalized gradient systems are proposed and the characteristics of the two systems are studied. The conditions under which a holonomic mechanical system can be considered as one of the two generalized gradient systems are obtained. The characteristics of the generalized gradient systems can be used to study the stability of the holonomic system. Some examples are given to illustrate the application of the results.
文摘Two new types of conserved quantities directly deduced by Mei symmetry of holonomic mechanical system are studied. The definition and criterion of Mei symmetry for holonomic system are given. A coordination function is introduced, the conditions under which the Mei symmetry can directly lead to the two types of conserved quantities and the forms of the two types of conserved quantities are obtained. An illustrative example is given. The result indicates that the coordination function can be selected properly according to the demand of the gauge function, thereby the gauge function can be found out more easily. Furthermore, since the choice of the coordination function has multiformity, much T more conserved quantity of Mei symmetry for holonomic mechanical system can be obtained.
文摘Based on the concept of adiabatic invariant,the perturbation to the Lie symmetry and adiabatic invariantsfor general holonomic mechanical systems are studied.The exact invariants induced directly from the Lie symmetryof the system without perturbation are given.The perturbation to the Lie symmetry is discussed and the adiabaticinvariants that have the different form from that in[Act.Phys.Sin.55(2006)3236(in Chinese)]of the perturbedsystem,are obtained.
文摘This paper uses Poincare’s formalism to study . the integral invariants of aconservative holonomic dynamical system Introducing new parameters for theasynchronous variation, a generalization of the poincare and Poincare-Cartan integralinvariants is presented.
文摘In this paper we use Poincaré’s equations in group variables to de- scribe the motion of a holonomic mechanical system and to determine Jacobi's mul- tiplier for the equations of motion.
