Bifibrations, in symplectic geometry called also dual pairs, play a relevant role in the theory of superintegrable Hamiltonian systems. We prove the existence of an analogous bifibrated geometry in dynamical systems with a symmetry group such that the reduced dynamics is periodic. The integrability of such systems has been proven by M. Field and J. Hermans with a reconstruction technique. We ap...

In this paper we develop results based on geometric mechanics to study the controllability of a class of controlled under-actuated left invariant mechanical systems on Lie groups. We exploit the invariance of the controlled nonlinear dynamics to the group action (symmetry) to derive a set of reduced dynamics for the system. We 3rst present su4cient conditions for the controllability of the redu...

W designing supply chains, firms are often faced with the competing demands of improved customer service and reduced cost. We extend a cost-based location-inventory model (Shen et al. 2003) to include a customer service element and develop practical methods for quick and meaningful evaluation of cost/service trade-offs. Service is measured by the fraction of all demands that are located within ...

The nonlinear system becomes an area with numerous investigations over the past decades. The conventional modal analysis could not be  applied on nonlinear continuous system which makes it impossible to construct the reduced order models and obtain system response based on limited number of measurement points. Nonlinear normal modes provide a useful tool for extending modal analysis to nonlinea...