arXiv subjects

Dino Boccaletti

Publications and source records attributed to Dino Boccaletti.

8 recordsLinked to original sources

arXiv2012

Raffaello Caverni (1837 - 1900) and the Society for the progress of the sciences: an independent priest criticized by the lay scientists

Raffaello Caverni, a Catholic priest, was a truly lay and anti-establishment intellectual in his opinions both on Darwin and on Galileo. He opposed the mythicization of Galileo, as a rule in Italy after the unification, even though he considered Galileo a great scientist. As a consequence the scientific community of that time, under the influence of Antonio Favaro, bitterly censured his work Storia del Metodo Sperimentale in Italia.In this way, Caverni's book was removed from the scientific debate in Italy for at least forty years.

physics.hist-ph↗

arXiv2008

Periodic orbits in the logarithmic potential

Analytic methods to investigate periodic orbits in galactic potentials. To evaluate the quality of the approximation of periodic orbits in the logarithmic potential constructed using perturbation theory based on Hamiltonian normal forms. The solutions of the equations of motion corresponding to periodic orbits are obtained as series expansions computed by inverting the normalizing canonical transformation. To improve the convergence of the series a resummation based on a continued fraction may be performed. This method is analogous to that looking for approximate rational solutions (Prendergast method). It is shown that with a normal form truncated at the lowest order incorporating the relevant resonance it is possible to construct quite accurate solutions both for normal modes and periodic orbits in general position.

astro-ph↗

arXiv2008

Quantitative predictions with detuned normal forms

The phase-space structure of two families of galactic potentials is approximated with a resonant detuned normal form. The normal form series is obtained by a Lie transform of the series expansion around the minimum of the original Hamiltonian. Attention is focused on the quantitative predictive ability of the normal form. We find analytical expressions for bifurcations of periodic orbits and compare them with other analytical approaches and with numerical results. The predictions are quite reliable even outside the convergence radius of the perturbation and we analyze this result using resummation techniques of asymptotic series.

nlin.CD↗

arXiv2008

Integrating the geodesic equations in the Schwarzschild and Kerr space-times using Beltrami's "geometrical" method

We revisit a little known theorem due to Beltrami, through which the integration of the geodesic equations of a curved manifold is accomplished by a method which, even if inspired by the Hamilton-Jacobi method, is purely geometric. The application of this theorem to the Schwarzschild and Kerr metrics leads straightforwardly to the general solution of their geodesic equations. This way of dealing with the problem is, in our opinion, very much in keeping with the geometric spirit of general relativity. In fact, thanks to this theorem we can integrate the geodesic equations by a geometrical method and then verify that the classical conservation laws follow from these equations.

gr-qc↗

arXiv2007

On the Orbit Structure of the Logarithmic Potential

We investigate the dynamics in the logarithmic galactic potential with an analytical approach. The phase-space structure of the real system is approximated with resonant detuned normal forms constructed with the method based on the Lie transform. Attention is focused on the properties of the axial periodic orbits and of low order `boxlets' that play an important role in galactic models. Using energy and ellipticity as parameters, we find analytical expressions of several useful indicators, such as stability-instability thresholds, bifurcations and phase-space fractions of some orbit families and compare them with numerical results available in the literature.

astro-ph↗

arXiv2006

Stability of axial orbits in galactic potentials

We investigate the dynamics in a galactic potential with two reflection symmetries. The phase-space structure of the real system is approximated with a resonant detuned normal form constructed with the method based on the Lie transform. Attention is focused on the stability properties of the axial periodic orbits that play an important role in galactic models. Using energy and ellipticity as parameters, we find analytical expressions of bifurcations and compare them with numerical results available in the literature.

nlin.CD↗

arXiv2005

Space-time trigonometry and formalization of the "Twin Paradox" for uniform and accelerated motions

The formal structure of the early Einstein's Special Relativity follows the axiomatic deductive method of Euclidean geometry. In this paper we show the deep-rooted relation between Euclidean and space-time geometries that are both linked to a two-dimensional number system: the complex and hyperbolic numbers, respectively. By studying the properties of these numbers together, pseudo-Euclidean trigonometry has been formalized with an axiomatic deductive method and this allows us to give a complete quantitative formalization of the twin paradox in a familiar "Euclidean" way for uniform motions as well as for accelerated ones.

physics.class-ph↗

arXiv2001

From the epicycles of the Greeks to Kepler's ellipse - The breakdown of the circle paradigm

The principle that celestial bodies must move on circular orbits or on paths resulting from the composition of circular orbits has been assumed as a constant guide in the astronomical thougth of the peoples facing the Mediterranean sea as from the second century B.C. until the beginning of the XVII century. The mathematical model based on such an assumption, the theory of epicycles in all its versions and modifications, has been taken as a scheme for all astronomical calculations during at least eighteen centuries, from Hipparcus to Kepler. As it is known, in Astronomia Nova (1609), Kepler succeded to establish the two laws which after him were named the first and the second Kepler's laws. The revolution he performed by giving up the circle paradigm is of fundamental importance and represents the indispensable premise to Newtonian theory. This revolution, the result of what Kepler called his "war" against Mars, is usually underestimated if one considers the break carried out with respect to the pre-Kepler celestial kinematics. In "Astronomia Nova" we assist to the attempt of Kepler to get for Mars an orbit consistent with the results of Tycho Brahe's observations. Passing through several phases and step by step discarding the hypoteses wich gave results in contrast with observations, Kepler arrived at establishing that the orbit of Mars around the Sun is an ellipse. Here an esposition is given of this work of analysis by Kepler wich is, in the history of science, one of the early examples of rigorous setting up of a model which correctly explains the experimental results.

physics.hist-ph↗