17 September 2001
Solar system dynamics has undergone a renaissance in the last decade, largely because of the wide availability of highly capable computers programmed with efficient numerical algorithms. The most commonly used algorithms have been made publicly available by H. F. Levison at Southwest Research Institute in Boulder, Colorado and Martin Duncan of Queen's University in Kingston, Ontario. Several of my students and post-doctoral fellows have profitably applied these techniques to various problems concerning the long-term evolution of the solar system. These codes have allowed us to track the histories of thousands of test particles that are gravitationally tugged by the major planets for times ranging from millions to billions of years. This set of software effectively forms a dynamical laboratory that can be used to understand how the solar system has come to have its present form.
In the mid-nineties, as part of his Ph.D. dissertation, Brett Gladman used a regularized mixed variable symplectic (RMVS) code developed as part of Levison and Duncan's SWIFT package; with it he studied the dynamical histories of lunar and martian ejecta in widely quoted work. He has subsequently gone on to investigate the delivery of meteorites from resonant locations in the main asteroid belt and the origin of fireballs. In his two years as a post-doc with me during the late nineties, Bill Bottke addressed three major problems, two of which involved lengthy numerical integrations. First, he studied the evolution of meteorites as perturbed by the planets, but also including a small Yarkovsky drag due to radiation recoil. For this, Bill incorporated the small Yarkovsky acceleration into the SWIFT RMVS3 integrator. Using the RMVS code, he also investigated the life cycles of Near Earth Asteroids in order to discover their numbers and origins so as to appreciate the hazard that they pose to Earth. Most recently one of my current students, Valerio Carruba, has been using various software packages developed by Levison to investigate the histories of asteroid families and the fate of hypothetical objects just barely captured about the giant planets.
These new techniques have truly revolutionized dynamical astronomy, but this would not have been true without Hal Levison's helpfulness. He has been willing to assist my students in getting started and to suggest improvements to their ideas. Hal's openness in sharing his software is exactly the scientific ideal, and in this way he has been an important role model for my students. Much excellent planetary dynamics has been performed using the SWIFT package.
Joseph A. Burns
I. P. Church Professor of Engineering and Professor of Astronomy
Cornell University
4 September 2001
I have been a heavy user of the SWIFT_RMVS series of codes since their creation in 1993, evolving through several versions, and sometime adapting the source code for particular idiosyncracies. I have used them for long-term integrations in the solar system to study meteorite transport, orbital stability of satellites around planets, and qualitative evolutions of comet orbits. Several of these scientific projects would have been impossible to tackle without the speed and efficiency of these software packages. The codes are very powerful, well written and documented, and (in my opinion) easy to use. They have become very heavily used worldwide in the field of solar system dynamics. I have found the authors extremely responsible towards the upkeep of the codes and providing information to the users.
Having said that, there are several structural issues about how the codes are written and how input/output is conducted that could benefit from a major re-write. Such a revision to a new language or structural conception will doubtless also allow non-negligible speed improvements. I believe that such a project would be of great utility to a world-wide audience of users of these algorithms.
Brett Gladman
Permanent Research Astronomer
Observatoire de la Cote d'Azur
23 August 2001
Swift is widely available and widely used. I have a student who will start using it in the Fall. To mind, it is an advanced course in Numerical Recipes. It is equivalent to Sverre Aarseth's widely distributed N-Body 1-6. Many of us would greatly benefit from an enhanced code.
Myron Lecar
Lecturer on Astronomy
Harvard-Smithsonian Center for Astrophysics
4 September 2001
Dear Hal:
It is my pleasure to write in support of your continued development of the SWIFT integration package for long-term integrations in planetary dynamics. The SWIFT integrators are first rate, and I have used them, usually in collaboration with you and/or Martin Duncan, to address various problems in planetary dynamics and planet formation. I have also read many interesting paper that you have written based on integrations with SWIFT.
As you generally make new portions of the codes available for use by the community within a few years of developing them, SWIFT has become the leading integration package for planetary dynamics problems, and many other groups have performed interesting research using SWIFT.
I strongly endorse your continued development of the code, including modernizing it to optimize results on parallel computers.
Sincerely,
Jack Lissauer
Space Scientist
Planetary Systems Branch
Space Science Division
NASA Ames Research Center
20 August 2001
I'm certainly willing to certify the importance that the swift package has had and still has in the planetary dynamics community. The package includes two main integrators: swift_mvs1 and swift_rmvs3, which are now largely in use by dynamicists and have become a standard in the field.
Swift_mvs integrates in a symplectic way the dynamics of planets and massless particles, provided that close encounters do not occur. The algorithm is due to Wisdom and Holman who, however, never distributed their code. I'm sure that the public availability of swift_mvs has boosted the use of symplectic integrations in celestial mechanics, which otherwise would have taken several years.
Swift_rmvs3 is an extension of swift_mvs that can deal with close encounters between massless particles and planets. Due to its high speed, this code allowed integrations of the evolution of thousands of bodies, from their source regions (resonances in the asteroid or in the Kuiper belt) to their ultimate dynamical fate (collision with the Sun or with a planet, or ejection on hyperbolic orbit). This has allowed studies of the origin, the dynamics and the steady state orbital distributions of meteoroids, Near Earth Asteroids and short periodic comets in a quantitative statistical sense.
A discussion of the revolutionary role that the swift package has had in celestial mechanics, and a review of the major results achieved with its use can be found in my paper for "Annual Reviews of Earth and Planetary Sciences", which will appear in 2002 but is downloadable from the page http://www.obs-nice.fr/morby/Invited_list.html.
Alessandro Morbidelli
Permanent Research Astronomer
Observatoire de la Cote d'Azur
13 September 2001
This letter is in support of continued development of the numerical code package SWIFT for the calculation of the long term evolution of n-body dynamical systems. SWIFT contains several types of programs including a Bulirsch-Stoer integrator, a fourth order T+U (TU4) method, but most importantly an algebraic routine that maps the system onto itself, which mapping integrates an n-body system much faster than conventional routines. The basic idea of using algebraic mappings of a system to speed the integration of the motions of bodies in the solar system was developed by Jack Wisdom and his colleagues a number of years ago. These mappings have become known as symplectic integrators or WHM (Wisdom-Holman Mapping) integrators, and the version published by Wisdom and Holman (1991) generalized the schemes to arbitrary configurations, where the integration times were typically reduced by more than a factor of 10 over the conventional integration schemes. These codes together with the increased speed of computers have at last enabled calculations of n-body configurations for times exceeding the age of the solar system with much less round-off and energy errors than conventional codes.
The Wisdom-Holman code was not freely distributed as a package, and it suffered a major deficiency of not handling close encounters between particles. Levison, Duncan and colleagues wrote a symplectic algebraic mapping code included in SWIFT that has been widely distributed in the dynamics community. SWIFT also includes a symplectic code for close encounters, but this latter code does not have a constant Hamiltonian, so energy is not necessarily bounded. Duncan, et al. developed a rather complicated algorithm that is a second symplectic code to accommodate close approaches, but this code maintains the other desirable properties of symplectic codes such as energy conservation and speed. This latter extension is called SyMBA (Symplectic Massive Body Algorithm) and I expect it to be eventually included in the SWIFT package. The freely available SWIFT package has become the choice of most serious workers in solar system dynamics, and the symplectic mapping codes therein have been responsible for revolutionizing evolutionary studies of solar system configurations involving many bodies. Without the ready availability of the symplectic mapping codes, problems involving the evolution of the swarm of cometary bodies and of the Kuiper belt of asteroids could never have been attempted. The codes have been a fundamental tool in studying the chaotic nature of solar system configurations, and in studies of the stability of the solar system.
In spite of SWIFT's astounding list of successful applications, there are still many problems that should be corrected such as its handling of input-output which can be very inefficient for all of the codes within SWIFT. The mapping codes have also not been accommodated for parallel processing. Any project that could further enhance this fundamental tool and broaden the range of problems for which its high speed and accuracy could be advantageously applied would be an excellent investment in the future of dynamical studies.
Stanton J. Peale
Professor of Physics Emeritus
Research Professor of Physics
University of California Santa Barbara
5 September 2001
The SWIFT-RMVS software package written by Hal Levison and Martin Duncan has been responsible for major advances in the past decade in our understanding of dynamical processes in the solar system. It has been successfully applied to such diverse problems as: the dynamical evolution of the Kuiper belt and the origin of the Jupiter family comets (Levison and Duncan 1994, 1997), the delivery of planetary ejecta and in particular, Martian meteorites, to the Earth and to other planets (Gladman et al. 1996, Gladman 1997), the evolution of the Jupiter Trojan asteroid swarms (Levison et al. 1997), cratering rates in the outer solar system (Zhanle et al. 1998), the formation of Uranus and Neptune (Thommes et al. 1999), the formation of the Oort cometary cloud surrounding the solar system (Dones et al. 2000), the origin of the Late Heavy Bombardment (Levison et al. 2001), and the origin of the Earth-crossing and Earth-approaching asteroids (Bottke et al. 2001). This software has been extremely valuable in that it allows accurate dynamical simulations which span the age of the solar system, and which permit close encounters with the perturbing planets and other bodies.
Moreover, the creators of this software have made it freely available to the scientific community so that it may be used to increase the productivity of many scientists with diverse interests, rather than keeping it as a specialized tool only for its creators. This openness has greatly expanded the range of problems to which the software has been applied, as evidenced by the many different authors cited above. The software is user-friendly and easy to install and test. Its creators have continually improved it and have made it available for a number of computing platforms and operating systems. It is probably one of the most useful tools we have today for studying the dynamics of the solar system.
Paul R. Weissman
Senior Research Scientist
Jet Propulsion Laboratory