On the long term numerical integration of planetary rings

2019 ◽  
Vol 354 ◽  
pp. 390-401 ◽  
Author(s):  
Juan F. Navarro ◽  
Juan Vargas
Keyword(s):  
Numerical Integration ◽  
Planetary Rings

Chaotic Motions of a Dual-Spin Body

1998 ◽  
Vol 65 (1) ◽  
pp. 150-156 ◽  
Author(s):  
A. C. Or
Keyword(s):  
Steady State ◽  
Numerical Integration ◽  
Coulomb Friction ◽  
Equations Of Motion ◽  
Homoclinic Tangency ◽  
Chaotic Attractors ◽  
Chaotic Motions ◽  
Homoclinic Points ◽  
Melnikov’S Method

The dynamics of a dual-spinner subject to the action of an internal oscillatory torque and Coulomb friction between the two linked bodies is investigated. The conditions for existence of transverse homoclinic points and homoclinic tangency of chaotic motions are obtained using Melnikov’s method. Through long-term numerical integration of the equations of motion, steady-state chaotic attractors are also found and studied numerically by varying the forcing amplitude.

scholarly journals New Methods for Long-Time Numerical Integration of Planetary Orbits

1992 ◽  
Vol 152 ◽  
pp. 395-406 ◽  
Author(s):  
Hiroshi Kinoshita ◽  
Hiroshi Nakai
Keyword(s):  
Angular Momentum ◽  
Numerical Integration ◽  
Planetary System ◽  
Symplectic Integrators ◽  
Truncation Errors ◽  
New Methods ◽  
Planetary Orbits ◽  
Long Time ◽  
Discretization Errors

When planetary orbits are numerically integrated for a long time by conventional integrators, the most serious problem is secular errors in the energy and the angular momentum of the planetary system due to discretization (truncation) errors. The secular errors in the energy and the angular momentum mean that the semi-major axes, the eccentricities, and the inclinations of planetary orbits have a secular error which grows linearly with time. Recently symplectic integrators and linear symmetric multistep integrators are found not to produce the secular errors in the energy and the angular momentum due to the discretization errors. Here we describe briefly both methods and discuss favorable properties of these integrators for a long-term integration of planetary orbits.

Algorithm for Evaluating the Hourly Radiation Utilizability Function

1983 ◽  
Vol 105 (3) ◽  
pp. 281-287 ◽  
Author(s):  
D. R. Clark ◽  
S. A. Klein ◽  
W. A. Beckman
Keyword(s):  
Solar Radiation ◽  
Numerical Integration ◽  
Simple Algorithm ◽  
Threshold Intensity ◽  
Analytical Expression ◽  
Monthly Average ◽  
Radiation Incident ◽  
Solar Radiation Incident ◽  
Radiation Measurements

A computationally simple algorithm is presented for evaluating the hourly utilizability function, φ, defined as the fraction of the long-term, monthly-average, hourly solar radiation incident on a surface which exceeds a specified threshold intensity. The algorithm was developed by correlating values of φ obtained by numerical integration of hourly radiation for three locations. The algorithm is shown to compare well both with a more complex analytical expression for φ developed recently and with results obtained numerically using many years of hourly horizontal radiation measurements in nine U.S. locations. In addition, the algorithm is shown to be applicable for surfaces of any orientation.

scholarly journals Some Aspects of Constructing Long Ephemerides of the Sun, Major Planets and the Moon: Ephemeris AE95

1997 ◽  
Vol 165 ◽  
pp. 245-250
Author(s):  
G.I. Eroshkin ◽  
N.I. Glebova ◽  
M.A. Fursenko ◽  
A. A. Trubitsina
Keyword(s):  
Mathematical Model ◽  
Solar System ◽  
Numerical Integration ◽  
High Precision ◽  
The Sun ◽  
Specific Character ◽  
The Moon ◽  
Special Edition ◽  
Polynomial Representation

The construction of long-term numerical ephemerides of the Sun, major planets and the Moon is based essentially on the high-precision numerical solution of the problem of the motion of these bodies and polynomial representation of the data. The basis of each ephemeris is a mathematical model describing all the main features of the motions of the Sun, major planets, and Moon. Such mathematical model was first formulated for the ephemerides DE/LE and was widely applied with some variations for several national ephemeris construction. The model of the AE95 ephemeris is based on the DE200/LE200 ephemeris mathematical model. Being an ephemeris of a specific character, the AE95 ephemeris is a basis for a special edition “Supplement to the Astronomical Yearbook for 1996–2000”, issued by the Institute of the Theoretical Astronomy (ITA) (Glebova et al., 1995). This ephemeris covering the years 1960–2010 is not a long ephemeris in itself but the main principles of its construction allow one to elaborate the long-term ephemeris on an IBM PC-compatible computer. A high-precision long-term numerical integration of the motion of major bodies of the Solar System demands a choice of convenient variables and a high-precision method of the numerical integration, taking into consideration the specific features of both the problem to be solved and the computer to be utilized.

scholarly journals Long-term and large-scale viscous evolution of dense planetary rings

Icarus ◽  
2010 ◽  
Vol 209 (2) ◽  
pp. 771-785 ◽  
Author(s):  
J. Salmon ◽  
S. Charnoz ◽  
A. Crida ◽  
A. Brahic
Keyword(s):  
Large Scale ◽  
Planetary Rings
Sign in / Sign up

Export Citation Format

Share Document