A consistent focus in theoretical mechanics has been on how to apply Lagrange's equation to continuum mechanics.This paper uses the concept of a variational derivative and its laws of operation to investigate the ...A consistent focus in theoretical mechanics has been on how to apply Lagrange's equation to continuum mechanics.This paper uses the concept of a variational derivative and its laws of operation to investigate the derivation of Lagrange's equation,which is then applied to nonlinear elasto-dynamics.In accordance with the work-energy principle and the energy conservation law,kinetic and potential energies are proposed for rigid-elastic coupling dynamics,whose governing equation is established by manipulating Lagrange's equation.In addition,case studies are used to demonstrate the application of the proposed method to spacecraft dynamics.展开更多
In this paper, the Poisson structures and Casimir functions, which play an important role in stability analysis of stationary motions, are given for a class of coupled rigid-elastic systems with symmetry-breaking. As ...In this paper, the Poisson structures and Casimir functions, which play an important role in stability analysis of stationary motions, are given for a class of coupled rigid-elastic systems with symmetry-breaking. As a practical example, the specific Casimir function is given for a rigid-elastic coupled body with a fixed point subjected to gravitational force. At last, a set of sufficient conditions for stability of stationary motions of a rigid-elastic body in a circular orbit are given by the energy-Casimir method.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
Planar motion for a rigid body with an elastic beam in a field of central gravitational force wasinvestigated, and both of the orbital motion and attitude motion were under consideration. The equations ofmotion of the...Planar motion for a rigid body with an elastic beam in a field of central gravitational force wasinvestigated, and both of the orbital motion and attitude motion were under consideration. The equations ofmotion of the system were derived by the variational principle, and on view point of generalized Hamiltoniandynamics, the sufficient conditions for the stability of one class of relative equilibria were given by the energy-momentum method.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.10272034)
文摘A consistent focus in theoretical mechanics has been on how to apply Lagrange's equation to continuum mechanics.This paper uses the concept of a variational derivative and its laws of operation to investigate the derivation of Lagrange's equation,which is then applied to nonlinear elasto-dynamics.In accordance with the work-energy principle and the energy conservation law,kinetic and potential energies are proposed for rigid-elastic coupling dynamics,whose governing equation is established by manipulating Lagrange's equation.In addition,case studies are used to demonstrate the application of the proposed method to spacecraft dynamics.
基金Project supported by the National Natural Science Foundation of China.
文摘In this paper, the Poisson structures and Casimir functions, which play an important role in stability analysis of stationary motions, are given for a class of coupled rigid-elastic systems with symmetry-breaking. As a practical example, the specific Casimir function is given for a rigid-elastic coupled body with a fixed point subjected to gravitational force. At last, a set of sufficient conditions for stability of stationary motions of a rigid-elastic body in a circular orbit are given by the energy-Casimir method.
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.
基金This work was supported by the National Natural Science Foundation of China(Grant No.19402005).
文摘Planar motion for a rigid body with an elastic beam in a field of central gravitational force wasinvestigated, and both of the orbital motion and attitude motion were under consideration. The equations ofmotion of the system were derived by the variational principle, and on view point of generalized Hamiltoniandynamics, the sufficient conditions for the stability of one class of relative equilibria were given by the energy-momentum method.
