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11.
S. Ferraz-Mello D. Nesvorný T.A. Michtchenko 《Celestial Mechanics and Dynamical Astronomy》1997,69(1-2):171-185
The lack of asteroids in the 2/1-resonance is explained by the global stochasticity of the solutions in the Sun-Jupiter-Saturn-asteroid
model. The explanation is based on data obtained with Laskar's frequency map analysis and on simulations showing the decisive
influence of Jupiter's orbit perturbations related to the "Great Inequality".
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
12.
S. Ferraz-Mello 《Celestial Mechanics and Dynamical Astronomy》1996,65(4):421-437
In the case of the 2:1 and 3:2 resonances with Jupiter, it has not been yet possible to have a complete identification of all chaotic diffusion processes at work, mainly because the time scale of some of them are of an order still out of the reach of precise integrations. A planar Hadjidemetriou's mapping, using expansions valid for high eccentricities and scaled in order to accelerate the diffusion processes, was derived. The solutions obtained with the mapping show huge eccentricity variations in all orbits starting in the middle of the 2:I resonance, when the main short-period perturbations of Jupiter's orbit are considered. The solutions starting in the middle of the 3:2 resonance do not show any important diffusion. 相似文献
13.
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15.
S. Ferraz-Mello C. Beaugé T. A. Michtchenko 《Celestial Mechanics and Dynamical Astronomy》2003,87(1-2):99-112
Numerical simulations of the evolution of planets or massive satellites captured in the 2/1 and 3/1 resonances, under the action of an anti-dissipative tidal force. The evolution of resonant trapped bodies show a richness of solutions: librations around stationary symmetric solutions with aligned periapses ( = 0) or anti-aligned periapses ( = ), librations around stationary asymmetric solutions in which the periapses configuration is fixed, but with taking values in a wide range of angles. Many of these solutions exist for large values of the eccentricities and, during the semimajor axes drift, the solutions show turnabouts from one configuration to another. The presented results are valid for other non-conservative anti-dissipative forces leading to adiabatic convergent migration and capture into one of these resonances. 相似文献
16.
S. Ferraz-Mello 《Celestial Mechanics and Dynamical Astronomy》2002,83(1-4):275-289
Explicit construction of the solutions of the Hamiltonian system given by H = H
0(J) – A(J) cos (ideal resonance problem), two orders of approximation beyond the well-known pendulum approximation. The given solutions are valid for libration amplitudes of order
. The procedure used is extended to allow the construction of the solutions of Hamiltonians with perturbations involving two degrees of freedom; the post-pendulum solution of an example of this kind is constructed. 相似文献
17.
T. A. Michtchenko C. Beaugé S. Ferraz-Mello 《Celestial Mechanics and Dynamical Astronomy》2006,94(4):411-432
We present a catalog of stable and unstable apsidal corotation resonance (ACR) for the resonant planar planetary three-body problem, including both symmetric and asymmetric solutions. Calculations are performed with a new approach based on a numerical determination of the averaged Hamiltonian function. It has the advantage of being very simple to use and, with the exception of the immediate vicinity of the collision curve, yields precise results for any values of the eccentricities and semimajor axes. The present catalog includes results for the 3/2, 3/1, and 4/1 mean-motion resonances. The 5/1 and 5/2 commensurabilities are also discussed briefly. These results complement our previous results for the 2/1 (Beaugé et al. 2006, MNRAS, 365, 1160–1170), and give a broad picture of the structure of many important planetary resonances. 相似文献
18.
A point relative to the application of the method of Hori to resonant systems is considered: For systems having one degree of freedom the topology of the phase plane of the auxiliary Hori's system is unaltered in the process of construction of a formal solution. The transformed Hamiltonian may not lead to singular points other than those included in the auxiliary Hori's Hamiltonian. 相似文献
19.
Carlos Roberto Sanquetta Ana Paula Dalla Corte Alexandre Behling Luani Rosa de Oliveira Piva Sylvio Péllico Netto Aurélio Lourenço Rodrigues Mateus Niroh Inoue Sanquetta 《Carbon balance and management》2018,13(1):25
Background
Biomass models are useful for several purposes, especially for quantifying carbon stocks and dynamics in forests. Selecting appropriate equations from a fitted model is a process which can involves several criteria, some widely used and others used to a lesser extent. This study analyzes six selection criteria for models fitted to six sets of individual biomass collected from woody indigenous species of the Tropical Atlantic Rain Forest in Brazil. Six models were examined and the respective fitted equations evaluated by the residual sum of squares, adjusted coefficient of determination, absolute and relative estimates of the standard error of estimate, and Akaike and Schwartz (Bayesian) information criteria. The aim of this study was to analyze the numeric behavior of these model selection criteria and discuss the ease of interpretation of them. The importance of residual analysis in model selection is stressed.Results
The adjusted coefficient of determination (\( R^{2}_{adj.} \)) and the standard error of estimate in percentage (Syx%) are relative model selection criteria and are not affected by sample size and scale of the response variable. The sum of squared residuals (SSR), the absolute standard error of estimate (Syx), the Akaike information criterion and the Schwartz information criterion, in turn, depend on these quantities. The best fit model was always the same within a given data set regardless the model selection criteria considered (except for SSR in two cases), indicating they tend to converge to a common result. However, such criteria are not always closely related across different data sets. General model selection criteria are indicative of the average goodness of fit, but do not capture bias and outlier effects. Graphical residual analysis is a useful tool to this detection and must always be used in model selection.Conclusions
It is concluded that the criteria for model selection tend to lead to a common result, regardless their mathematical formulation and statistical significance. Relative measures of goodness of fitting are easier to interpret than the absolute ones. Careful graphical residual analysis must always be used to confirm the performance of the models.20.
Sylvio Ferraz-Mello 《Celestial Mechanics and Dynamical Astronomy》2013,116(2):109-140
This paper presents a new theory of the dynamical tides of celestial bodies. It is founded on a Newtonian creep instead of the classical delaying approach of the standard viscoelastic theories and the results of the theory derive mainly from the solution of a non-homogeneous ordinary differential equation. Lags appear in the solution but as quantities determined from the solution of the equation and are not arbitrary external quantities plugged in an elastic model. The resulting lags of the tide components are increasing functions of their frequencies (as in Darwin’s theory), but not small quantities. The amplitudes of the tide components depend on the viscosity of the body and on their frequencies; they are not constants. The resulting stationary rotations (often called pseudo-synchronous) have an excess velocity roughly proportional to $6ne^2/(\chi ^2+\chi ^{-2})$ ( $\chi $ is the mean-motion in units of one critical frequency—the relaxation factor—inversely proportional to the viscosity) instead of the exact $6ne^2$ of standard theories. The dissipation in the pseudo-synchronous solution is inversely proportional to $(\chi +\chi ^{-1})$ ; thus, in the inviscid limit, it is roughly proportional to the frequency (as in standard theories), but that behavior is inverted when the viscosity is high and the tide frequency larger than the critical frequency. For free rotating bodies, the dissipation is given by the same law, but now $\chi $ is the frequency of the semi-diurnal tide in units of the critical frequency. This approach fails, however, to reproduce the actual tidal lags on Earth. In this case, to reconcile theory and observations, we need to assume the existence of an elastic tide superposed to the creeping tide. The theory is applied to several Solar System and extrasolar bodies and currently available data are used to estimate the relaxation factor $\gamma $ (i.e. the critical frequency) of these bodies. 相似文献