arXiv subjects

Clodoaldo Ragazzo

Publications and source records attributed to Clodoaldo Ragazzo.

7 recordsLinked to original sources

arXiv2026

An angular-momentum preserving dissipative model for the point-mass N -body problem

A simple mathematical model emulating energy dissipation due to tidal effects is proposed. In this model, forces acting between masses remove energy but preserve the total angular momentum of the system. We study the effect of such forces on the particular family of orbits in central configurations, and show that a specific dependence on the mutual distances between the bodies leads to homographic equations equivalent to those of the two-body problem with dissipation. We then describe in detail the topology of solutions of the dissipative two-body system via Poincaré compactification. Finally, we present equations averaged over Keplerian motion showing no influence of the dissipation on periapsis precession.

nlin.CD↗

arXiv2026

Droplet rebounds off a fluid bath at low Weber numbers

We present a method to simulate non-coalescing impacts and rebounds of droplets onto the free surface of a liquid bath, together with new experimental data, focused on the low-speed impact of droplets. The method is derived from first principles and imposes only natural geometric and kinematic constraints on the motion of the impacting interfaces, yielding predictions for the evolution of the contact area, pressure distribution, and wave field generated on both impacting masses. This work generalises an existing kinematic-match method whose prior applications dealt with deformation of the surface of the bath only; i.e., neglecting that of the droplet. The method's extension to include droplet deformation gives predictions that compare favourably with existing experimental results and our new experiments conducted in the low-Weber-number regime.

physics.flu-dyn↗

arXiv2024

Tidal Evolution and Spin-Orbit Dynamics: The Critical Role of Rheology

This study analyzes secular dynamics using averaged equations that detail tidal effects on the motion of two extended bodies in Keplerian orbits. It introduces formulas for energy dissipation within each body of a binary system. The equations, particularly in contexts like the Sun-Mercury system, can be delineated into a fast-slow system. A significant contribution of this work is the demonstration of the crucial role complex rheological models play in the capture by spin-orbit resonances. This is particularly evident in the notable enlargement of the basin of attraction for Mercury's current state when transitioning from a single characteristic time rheology to a dual characteristic time model, under the constraint that both models comply with the same estimate of the complex Love number at orbital frequency. The study also underscores the importance of Mercury's elastic rigidity on secular timescales.

astro-ph.EP↗

arXiv2024

Spin-Orbit Synchronization and Singular Perturbation Theory

In this study, we formulate a set of differential equations for a binary system to describe the secular-tidal evolution of orbital elements, rotational dynamics, and deformation (flattening), under the assumption that one body remains spherical while the other is slightly aspherical throughout the analysis. By applying singular perturbation theory, we analyze the dynamics of both the original and secular equations. Our findings indicate that the secular equations serve as a robust approximation for the entire system, often representing a slow-fast dynamical system. Additionally, we explore the geometric aspects of spin-orbit resonance capture, interpreting it as a manifestation of relaxation oscillations within singularly perturbed systems.

astro-ph.EP↗

arXiv2023

Equivalence between simple multilayered and homogeneous laboratory-based rheological models in planetary science

The goal of this work is to investigate under which circumstances the tidal response of a stratified body can be approximated by that of a homogeneous body. We show that any multilayered planet model can be approximated by a homogeneous body, with the same dissipation of tidal energy as a function of the excitation frequency, as long as the rheology of the homogeneous model is sufficiently complex. Moreover we provide two straightforward methods for finding the parameters of the homogeneous rheology that would exhibit the same tidal response as the layered body. These results highlight the fact that the two models cannot be distinguished from each other only by the measurement of the second degree tidal Love number and quality factor, and that we do not need the complexity of the multilayer planet model in order to estimate its tidal dissipation. The methodology promises a great simplification of the treatment of multilayered bodies in numerical simulations because the treatment of a homogeneous body -- even with a complex rheological model -- can be computationally better handled than that of a multilayered planet.

astro-ph.EP↗

arXiv2022

Librations of a body composed of a deformable mantle and a fluid core

We present fully three-dimensional equations to describe the rotations of a body made of a deformable mantle and a fluid core. The model in its essence is similar to that used by INPOP (Integration Planétaire de l'Observatoire de Paris), e.g. Viswanathan et al. (2019), and by JPL (Jet Propulsion Laboratory), e.g. Folkner et al. (2014), to represent the Moon. The intended advantages of our model are: straightforward use of any linear-viscoelastic model for the rheology of the mantle; easy numerical implementation in time-domain (no time lags are necessary); all parameters, including those related to the "permanent deformation", have a physical interpretation. The paper also contains: 1) A physical model to explain the usual lack of hydrostaticity of the mantle (permanent deformation). 2) Formulas for free librations of bodies in and out-of spin-orbit resonance that are valid for any linear viscoelastic rheology of the mantle. 3) Formulas for the offset between the mantle and the idealized rigid-body motion (Peale's Cassini states). 4) Applications to the librations of Moon, Earth, and Mercury that are used for model validation.

astro-ph.EP↗

arXiv2019

Andrade rheology in time-domain. Application to Enceladus' dissipation of energy due to forced libration

The main purpose of this work is to present a time-domain implementation of the Andrade rheology, instead of the traditional expansion in terms of a Fourier series of the tidal potential. This approach can be used in any fully three dimensional numerical simulation of the dynamics of a system of many deformable bodies. In particular, it allows large eccentricities, large mutual inclinations, and it is not limited to quasi-periodic perturbations. It can take into account an extended class of perturbations, such as chaotic motions, transient events, and resonant librations. The results are presented by means of a concrete application: the analysis of the libration of Enceladus. This is done by means of both analytic formulas in the frequency domain and direct numerical simulations. We do not a priori assume that Enceladus has a triaxial shape, the eventual triaxiality is a consequence of the satellite motion and its rheology. As a result we obtain an analytic formula for the amplitude of libration that incorporates a new correction due to the rheology. Our results provide an estimation of the amplitude of libration of the core of Enceladus as 0.6% of that of the shell. They also reproduce the observed 10 GW of tidal heat generated by Enceladus with a value of $0.17\times 10^{14}$Pa$\cdot$s for the global effective viscosity under both Maxwell and Andrade rheology.

astro-ph.EP↗