We firstly intoruduced a kind of special functions and a kind of special Poisson bracket on a product manifold,then give a kind of special generalized Hamiltonian vector fields by using the special Poisson bracket.Mor...We firstly intoruduced a kind of special functions and a kind of special Poisson bracket on a product manifold,then give a kind of special generalized Hamiltonian vector fields by using the special Poisson bracket.Moreover,we give a method to compose a new generalized Hamiltonian system on the Poisson product manifold by using two known generalized Hamitonian systems on the factor Poisson manifolds.We also discuss the conservative properties of the new composed generalized Hamiltonian systems as well as the relation between the Poisson mapping on the Poisson product manifold and that on the factor Poisson manifolds.展开更多
Hamiltonian structure of a rigid body in a circular orbit is established in this paper. With the reduction technique, the Hamiltonian structure of a rigid body in a circular orbit is derived from Lie-Poisson structure...Hamiltonian structure of a rigid body in a circular orbit is established in this paper. With the reduction technique, the Hamiltonian structure of a rigid body in a circular orbit is derived from Lie-Poisson structure of semidirect product, and Hamiltonian is derived from Jacobi's integral. The above method can be generalized to establish the Hamiltonian structure of a rigid body with a flexible attachment in a circular or- bit. At last, an example of stability analysis is given.展开更多
文摘We firstly intoruduced a kind of special functions and a kind of special Poisson bracket on a product manifold,then give a kind of special generalized Hamiltonian vector fields by using the special Poisson bracket.Moreover,we give a method to compose a new generalized Hamiltonian system on the Poisson product manifold by using two known generalized Hamitonian systems on the factor Poisson manifolds.We also discuss the conservative properties of the new composed generalized Hamiltonian systems as well as the relation between the Poisson mapping on the Poisson product manifold and that on the factor Poisson manifolds.
基金The projeet supported by National Natural Science Foundation of China and Aeronautic Science Foundation.
文摘Hamiltonian structure of a rigid body in a circular orbit is established in this paper. With the reduction technique, the Hamiltonian structure of a rigid body in a circular orbit is derived from Lie-Poisson structure of semidirect product, and Hamiltonian is derived from Jacobi's integral. The above method can be generalized to establish the Hamiltonian structure of a rigid body with a flexible attachment in a circular or- bit. At last, an example of stability analysis is given.
