1,354,606 research outputs found
Perturbations of Superintegrable Hamiltonian Systems
No full textThis is a review of the structure of superintegrable (or noncommutatively integrable) Hamiltonian systems and of the dynamics of their perturbations
Sensitivity Analysis for Environmental Models and Monitoring Networks
No full textStatistical sensitivity analysis is shown to be a useful technique for assessing both multivariate environmental computer models and environmental statistical spatio-temporal models in the perspective of risk assessment. Methods are reviewed and extended to cover with two applications which are reported as case studies. The first, related to waste water biofilters for heavy metals, is aimed at assessing the input influence on both environmental and economical variables. The second, related to spatio-temporal models for air quality monitoring networks, is intended to study the influence of each station to the model performance
The influence of the situation on the distributed leadership of curriculum : A Queensland secondary schooling case
No full textFasso, W ORCiD: 0000-0002-0711-7258"This thesis uses the distributed leadership framework to investigate the distributed leadership of the implementation of a new curriculum by teachers in a Queensland regional state secondary science department"--Abstract
A "changing chart" symplectic algorithm for rigid bodies and other Hamiltonian systems on manifolds
No full textWe revive the elementary idea of constructing symplectic integrators for Hamiltonian flows on manifolds by covering the manifold with the charts of an atlas, implementing the algorithm in each chart ( thus using coordinates) and switching among the charts whenever a coordinate singularity is approached. We show that this program can be implemented successfully by using a splitting algorithm if the Hamiltonian is the sum H-1 + H-2 of two (or more) integrable Hamiltonians. Profiting from integrability, we compute exactly the flows of H-1 and H-2 in each chart and thus compute the splitting algorithm on the manifold by means of its representative in any chart. This produces a symplectic algorithm on the manifold which possesses an interpolating Hamiltonian, and hence it has excellent properties of conservation of energy. We exemplify the method for a point constrained to the sphere and for a symmetric rigid body under the influence of positional potential forces
Periodic flows, rank-two Poisson structures, and nonholonomic mechanics
No full textIt has been recently observed that certain (reduced) nonholonomic systems are Hamiltonian with respect to a rank-two Poisson structure. We link the existence of these structures to a dynamical property of the (reduced) system: its periodicity, with positive period depending continuously on the initial data. Moreover, we show that there are in fact infinitely many such Poisson structures and we classify them. We illustrate the situation on the sample case of a heavy ball rolling on a surface of revolution
HAMILTONIAN PERTURBATION-THEORY ON A MANIFOLD
No full textAbstract: This paper deals with Hamiltonian perturbation theory for systems which, like Euler-Poinsot (the rigid body with a fixed point and no torques), are degenerate and do not possess a global system of action-angle coordinates. It turns out that the usual methods of perturbation theory, which are essentially 'local' being based on the construction of normal forms within the domain of a local coordinate system, are not immediately usable to study perturbations of these systems, since degeneracy makes impossible to control that the system does not fall into a singularity of the coordinates. To overcome this difficulty, we develop a 'global' formulation of Hamiltonian perturbation theory, in which the normal forms are globally defined on the phase space manifold. The key for this study lies in the geometry of the fibration by the invariant tori of an integrable degenerate Hamiltonian system, which is described by some generalizations of the Liouville-Arnol'd theorem and is reviewed in the paper. As an application, we provide a 'global' formulation of Nekhoroshev's theorem on the stability for exponentially long times
On a relation among Lie series
No full textAbstract: In this paper we discuss the relation between the structures of the series expansion for the Dragt and Finn composition of Lie transforms and for a transformation introduced by Giorgilli and Galgani. A recursive algorithm is presented which is used to generate the series expansion for the composition of Lie transforms. This algorithm strongly resembles the algorithm of Giorgilli and Galgani, and differs from it only in an ordering property. The relation with the algorithms of Kamel and Henrard for Deprit's direct and inverse series is also discussed
The Euler-Poinsot top: A non-commutatively integrable system without global action-angle coordinates
No full textAbstract: We study the global structure of the fibration by the invariant two-dimensional tori of the Euler-Poinsot top-the rigid body with a fixed point and no torques. We base our analysis on the notion of bifibration (or dual pair) which, as results from the approach based on the so-called non-commutative integrability, provides a thorough description of the geometry of integrable degenerate Hamiltonian systems. In this way, we get a global geometric picture of the Euler-Poinsot system which fully accounts for its degeneracy through the (Poisson) structure? of the base of the fibration by the two-dimensional invariant tori. In particular, we explain in this way why this system does not possess global 'generalized' action-angle coordinates: the obstructions are the topological non-triviality of the fibration by the invariant two-dimensional tori and the compactness of the symplectic leaves of its base manifold. We also compare this description with the usual description based on the notion of complete integrability, and we remark that, as a general fact, such a common approach fails to provide a natural, thorough description of degenerate systems
Regular and chaotic motions of the fast rotating rigid body: a numerical stydy
No full textWe numerically investigate the dynamics of a symmetric rigid body with a fixed point in a small analytic external potential (equivalently, a fast rotating body in a given external field) in the light of previous theoretical investigations based on Nekhoroshev theory. Special attention is posed on "resonant" motions, for which the tip of the unit vector mu in the direction of the angular momentum vector can wander, for no matter how small epsilon, on an extended, essentially two-dimensional, region of the unit sphere, a phenomenon called "slow chaos". We produce numerical evidence that slow chaos actually takes place in simple cases, in agreement with the theoretical prediction. Chaos however disappears for motions near proper rotations around the symmetry axis, thus indicating that the theory of these phenomena still needs to be improved. An heuristic explanation is proposed
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