IRIS Università degli Studi di Bolognahttps://cris.unibo.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Fri, 17 Sep 2021 18:36:30 GMT2021-09-17T18:36:30Z10321Closed form Solution to Nonlinear Equilibria and Oscillations of a Damped Eccentric Rotorhttp://hdl.handle.net/11585/382721Titolo: Closed form Solution to Nonlinear Equilibria and Oscillations of a Damped Eccentric Rotor
Abstract: We study an eccentric and elastically damped rotor from both a statical and dynamical point of view. The system, whose genesis is in the re-loading mechanism of an automatic watch, behaves like a generalized physical pendulum with the addition of eccentricity and damping. The static analysis is performed by settling the statical equilibria and defining their nature, whose effective computation can be done numerically.
The dynamical analysis leads to a nonlinear differential initial-value problem whose integration is carried out by means of Jacobi elliptic functions. It reveals that, starting from both positional and kinetic zero initial conditions, only periodical motions, see formulae (4.8) or (4.13), are allowed and all confined inside a potential well. Closed form expressions of the oscillation period have been obtained through complete elliptic integrals of the first kind. In such a way a further treatment is added to the non-rich collection of 1-D nonlinear oscillators suitable of closed form integration.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11585/3827212014-01-01T00:00:00ZExact curvature elastica of a thin cantilever under terminal loadshttp://hdl.handle.net/11585/69989Titolo: Exact curvature elastica of a thin cantilever under terminal loads
Abstract: A thin, flexible, one side-built-in rod under a concentrated terminal force
is studied in its elastic equilibrium configuration. In order to make the
problem more tractable, a proper set of state variables is chosen, facing
with a second order, nonlinear, but textit{autonomous} boundary value
problem, in the rotation phi pertaining to each s-section. The
search of the free end rotation phi0, following the isoperimetric
assumption, leads to a numerical sub-problem inside the main BVP.
Furthermore, if x(s) and y(s) mean the elastica coordinates parametrized
on the arclength s, one obtains x'(s) and y'(s) as elliptic functions of s. Finally, some minor changes have been shown in
order to pass from a loading force to a more general free-end load
combination, consisting of a force and a couple.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/11585/699892008-01-01T00:00:00ZNonlinear Dynamics of a Two-Degree of Freedom Hamiltonian System: Bifurcation and Integrationhttp://hdl.handle.net/11585/62454Titolo: Nonlinear Dynamics of a Two-Degree of Freedom Hamiltonian System: Bifurcation and Integration
Abstract: In this paper we treat the motion induced by a starting pulse on
a system of two-degrees of freedom. Decoupling the motion equations, we obtain the a nonlinear ordinary diﬀerential equation which is integrated by means of the Jacobi elliptic functions
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/11585/624542008-01-01T00:00:00ZEOQ when holding costs grow with the stock level: well-posedness and solutionshttp://hdl.handle.net/11585/62584Titolo: EOQ when holding costs grow with the stock level: well-posedness and solutions
Abstract: An existence-uniqueness theorem is proved about a minimum cost order for a class of inventory models whose holding costs grow, following a power law, with the stock level. The theorem requires to perform a check of convergence of some improper integrals, and constitutes the article's main theoretical contribution to the subject. As application, several cases of demand are considered as functions of the stock level.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/11585/625842008-01-01T00:00:00ZPLANAR BRACHISTOCHRONE OF A PARTICLE ATTRACTED IN VACUO BY AN INFINITE RODhttp://hdl.handle.net/11585/75589Titolo: PLANAR BRACHISTOCHRONE OF A PARTICLE ATTRACTED IN VACUO BY AN INFINITE ROD
Abstract: The authors analyze the planar brachistochrone in vacuo under the attraction of an infinite rod, adding a new closed form treatment to the known solutions’ collection. Accordingly, a nonlinear boundary value problem is solved after solution’s existence and uniqueness are proved noticing that the variational integrand meets the conditions of a Cesari’s theorem. This problem, proposed by G. T. Tee in "Brachistochrones for attractive logarithmic potential" New Zealand Journal of Mathematics 30, No.2, 183–196 (2001) and treated numerically, is solved here in closed form. The trajectory’s parametric equations are obtained by means
of a generalized, 2-variables, hypergeometric Lauricella confluent function, for the first time used in optimization.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/11585/755892007-01-01T00:00:00ZStraight and circular motions of a particle in the
field of two fixed attractorshttp://hdl.handle.net/11585/62452Titolo: Straight and circular motions of a particle in the
field of two fixed attractors
Abstract: The two centre problem is studied both in the phase plane and in
spacetime, assuming ﬁrst a trajectory collinear, and, as a second case, a circular one through the newtonian attractors, ﬁnding a saddle equilibrium. For the latter problem a probably new differential equation is met and solved. Time is then obtained in both cases through elliptic integrals of all kinds and Jacobian functions.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/11585/624522008-01-01T00:00:00ZReply of the Authors to Prof. Neukirch commentshttp://hdl.handle.net/11585/80408Titolo: Reply of the Authors to Prof. Neukirch comments
Abstract: The side comments of Professor Neukirch come after several (unfruitful) personal communications: now he keeps out from his own papers, focusing his claims on paper Tobias I, Coleman BD, Olson WK (1994) The depen- dence of DNA tertiary structure on end conditions: theory and implications for topological transitions. J Chem Phys 101(12):10990–10996
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/11585/804082007-01-01T00:00:00ZThe meridian curve of a wetting drop: a boundary value problem and its elliptic integrals solutionhttp://hdl.handle.net/11585/389303Titolo: The meridian curve of a wetting drop: a boundary value problem and its elliptic integrals solution
Abstract: In this article we study the shape of free surfaces of a static fluid under gravity. We consider the meridian curve of a heavy liquid drop standing on a horizontal base: the main assumption concerns the liquid wetting capability, namely its contact angle well below pi/2. The nonlinear differential boundary problem is solved through the shooting method. Our treatment is self-consistent as holding all demonstrations of existence, uniqueness, and computability. We conclude providing the eigenvalues set to the radius and the meridian curve of the drop through elliptic integrals: such a new exact solution—see (3.9) and (3.10) —is enriching the literature on capillarity.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11585/3893032014-01-01T00:00:00ZEOQ under exogenous and periodic demandhttp://hdl.handle.net/11585/75770Titolo: EOQ under exogenous and periodic demand
Abstract: In this paper we give a sufficient condition for the existence of the economic batch to a Wilson-type inventory model loaded by a fully exogenous continuous demand function of time. After some cases solvable in closed form, the computational problem is introduced of inverting the reordering time versus the ordered quantity as necessary step to obtain the cost function to be minimized. Such a mixed (theoretical/numerical) approach is applied to a demand consisting of three different behaviors: growth, decrease and prolonged zero. Such a wave-form is assumed to iterate itself periodically and the relevant seasonal demand is expanded in a Fourier series of time. Performing the integration and reverting the reordering time, the cost function is computed and its minimizing EOQ detected. Finally an example shows that the above conditions guarantee the existence but not uniqueness to solution.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/11585/757702009-01-01T00:00:00ZMathematical properties of EOQ models with special cost structurehttp://hdl.handle.net/11585/133755Titolo: Mathematical properties of EOQ models with special cost structure
Abstract: An existence-uniqueness theorem is proved about a minimum cost order for a class of inventory models whose holding costs grow according to a stock level power law. The outcomes of a previous work of two of the authors are then extended to different environments: i.e. when the holding costs change during time generalizing the Weiss model, or with invariable holding costs but adopting a backordering strategy. Application cases are provided assuming several functional behaviors of demand versus the stock level
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/11585/1337552013-01-01T00:00:00Z