About the stability of nonconservative undamped elastic systems:some new elements

International audienceIt is well-known that the domains of static stability and dynamic stability (even for a linear approach) do not match each other when the system is no more conservative and the dynamic approach is usually privileged, meaning that the dynamic stability domain is included in the static one. Following previous works proposing a new criterion of static stability of nonconservative systems and prolonging a paper of Gallina devoted to linear dynamic instability (flutter), we show in this paper some remarkable relations between the two approaches: contrary to the common thought, the new static stability criterion implies partially the dynamic one

Bifurcation diagrams for Hamiltonian nilpotent centers of linear plus cubic homogeneous polynomial vector fields

Agraïments: The third author is partially supported by FCT/Portugal through UID/MAT/04459/2013Following the work done in [8] we provide the bifurcation diagrams for the global phase portraits in the Poincaré disk of all Hamiltonian nilpotent centers of linear plus cubic homogeneous planar polynomial vector fields

О стабилизации неустойчивого вращения свободного волчка Лагранжа с жидкостью

Розглянуто задачу про стійкість та стабілізацію нестійкого обертання вільного вовчка Лагранжа з довільною осесиметричною порожниною, що містить ідеальну рідину. В рамках необхідних умов стійкості аналітично показано можливість стабілізації за допомогою твердих тіл, що обертаються. Числові розрахунки підтвердили результати аналітичних досліджень для вовчка з еліпсоідальною та циліндричною порожнинами.A problem on stability and stabilization of unstable rotation of the Lagrange free top with arbitrary axisymmetric cavity filled by an ideal fluid is considered. Within the framework of necessary conditions of stability, a possibility is shown to stabilize using the rotating rigid bodies. The numerical calculations endorse the analytical results for the top with ellipsoidal and cylindrical cavit

Program Verification by Using DISCOVERER

Recent advances in program verification indicate that various verification problems can be reduced to semi-algebraic system (SAS for short) solving. An SAS consists of polynomial equations and polynomial inequalities. Algorithms for quantifier elimination of real closed fields are the general method for those problems. But the general method usually has low efficiency for specific problems. To overcome the bottleneck of program verification with a symbolic approach, one has to combine special techniques with the general method. Based on the work of complete discrimination systems of polynomials [33,31], we invented new theories and algorithms [32,30,35] for SAS solving and partly implemented them as a real symbolic computation tool in Maple named DISCOVERER. In this paper, we first summarize the results that we have done so far both on SAS-solving and program verification with DISCOVERER, and then discuss the future work in this direction, including SAS-solving itself, termination analysis and invariant generation of programs, and reachability computation of hybrid systems etc. ? IFIP International Federation for Information Processing 2008.EI