Based on the concept of adiabatic invariant,the perturbation to Noether-Lie symmetry and adiabatic invariants for mechanical systems in phase space are studied.The criterion of the Noether-Lie symmetry for the perturb...Based on the concept of adiabatic invariant,the perturbation to Noether-Lie symmetry and adiabatic invariants for mechanical systems in phase space are studied.The criterion of the Noether-Lie symmetry for the perturbed system is given,and the definition of the perturbation to Noether-Lie symmetry for the system under the action of small disturbance is presented.Meanwhile,the Noether adiabatic invariants and the generalized Hojman adiabatic invariants of the perturbed system are obtained.展开更多
We investigated the vibration of a cleaning robot for hotline insulators, providing a flexible elevating link with a rigid moving link at the end. A Lagrange dynamic model is established based on the assumed mode meth...We investigated the vibration of a cleaning robot for hotline insulators, providing a flexible elevating link with a rigid moving link at the end. A Lagrange dynamic model is established based on the assumed mode method. An approach is proposed to reduce residual vibration of the flexible elevating link by optimizing acceleration of rigid link using the Pontryagin maximum principle (PMP). A numerical solution to the proposed optimization problem including a two-point boundary-value problem (2PBVP) is developed. Residual vibration of the flexible elevating link of the optimal acceleration profile is compared with that of the optimal trapezoid velocity profile. The result shows that the proposed trajectory optimization method can reduce the residual vibration more effectively.展开更多
文摘Based on the concept of adiabatic invariant,the perturbation to Noether-Lie symmetry and adiabatic invariants for mechanical systems in phase space are studied.The criterion of the Noether-Lie symmetry for the perturbed system is given,and the definition of the perturbation to Noether-Lie symmetry for the system under the action of small disturbance is presented.Meanwhile,the Noether adiabatic invariants and the generalized Hojman adiabatic invariants of the perturbed system are obtained.
文摘We investigated the vibration of a cleaning robot for hotline insulators, providing a flexible elevating link with a rigid moving link at the end. A Lagrange dynamic model is established based on the assumed mode method. An approach is proposed to reduce residual vibration of the flexible elevating link by optimizing acceleration of rigid link using the Pontryagin maximum principle (PMP). A numerical solution to the proposed optimization problem including a two-point boundary-value problem (2PBVP) is developed. Residual vibration of the flexible elevating link of the optimal acceleration profile is compared with that of the optimal trapezoid velocity profile. The result shows that the proposed trajectory optimization method can reduce the residual vibration more effectively.
