发表机构
University of Washington; Institute of Applied Astronomy of the Russian Academy of Sciences; NSF-DOE Vera C. Rubin Observatory/NSF NOIRLab; The Grainger College of Engineering Department of Aerospace Engineering, University of Illinois Urbana-Champaign（华盛顿大学; 俄罗斯科学院应用天体物理研究所; 美国国家科学基金会-能源部薇拉·C·鲁宾天文台/美国国家科学基金会NOIRLab; 伊利诺伊大学厄巴纳-香槟分校格雷格工程学院航空航天工程系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出改进的Lobatto配置积分器Lobbie，在多个太阳系长期积分基准测试中表现出优异的稳定性和效率，能量守恒达10^-14，优于IAS15并接近WHFast速度，是传统辛映射和Gauss-Radau方法的强大通用替代方案。
AI 中文摘要
高效且精确的数值积分方法是研究太阳系长期动力学的基础，因为数值误差可能在数十亿个轨道周期内累积。在本工作中，我们研究了我们对Lobbie的改进版本的性能，Lobbie是一种用于太阳系长期模拟的Lobatto配置积分器。我们将Lobbie与广泛使用的WHFast辛积分器以及Rebound包中实现的高阶自适应配置积分器IAS15进行了比较。积分器的性能通过五个基准问题进行评估：一个圆形二体轨道积分100 Myrs；偏心率达到1-10^{-6}的二体轨道，用于测试在反复近距离接触期间的自适应步长控制；完整的八行星太阳系积分100 Myrs；四颗巨行星积分10 Gyrs；以及八行星太阳系连同50颗阿登型轨道小行星积分1 Myr，以测试积分器在混沌、充满近距离接触环境中的一致性。在所有测试中，Lobbie表现出优异的长期稳定性和有竞争力的计算性能。对于完整的太阳系积分，Lobbie实现了10^{-14}量级的相对能量守恒，同时在计算效率上优于IAS15，并在相当精度下接近WHFast的速度。在太阳系加小行星的测试中，Lobbie还使木星轨道的不同实现之间在1 Myr积分后保持约1.5 km以内的一致性，比IAS15好两个数量级，并且速度快两倍。我们的结果表明，Lobbie为天体力学中的长期动力学模拟提供了一种强大的通用替代方案，可替代传统的辛映射或Gauss-Radau配置方法。
英文摘要
Efficient and accurate numerical integration methods are fundamental to studying long-term solar system dynamics, where numerical errors can accumulate over billions of orbital periods. In this work, we investigate the performance of our modification of Lobbie, a Lobatto collocation integrator for long-term simulations of the Solar System. We compare Lobbie against the widely used WHFast symplectic integrator and the high-order adaptive collocation integrator IAS15 implementations in the Rebound package. The performance of the integrator is evaluated using five benchmark problems: a circular two-body orbit integrated over 100 Myrs, two-body orbits with eccentricities up to 1-10^{-6} to test the adaptive step size control during repeated close encounters, the full eight-planet Solar System integrated over 100 Myrs, the four giant planets integrated over 10 Gyrs, and the eight-planet Solar System together with 50 asteroids on Aten-like orbits integrated over 1Myr to test the integrator's consistency in a chaotic, close-encounter-rich environment. Across all tests, Lobbie demonstrates excellent long-term stability and competitive computational performance. For full Solar System integrations, Lobbie achieves relative energy conservation at the level of 10^{-14} while outperforming IAS15 in computational efficiency and approaching the speed of WHFast at comparable accuracy. In the Solar System plus asteroids test, Lobbie also keeps different realizations of Jupiter's orbit consistent with each other to within about 1.5 km after 1 Myr of integration, two orders of magnitude better than IAS15, being twice faster. Our results demonstrate that Lobbie provides a powerful universal alternative to traditional symplectic mappings or Gauss-Radau collocation methods for long-term dynamical simulations in celestial mechanics.
Comments12 pages, 8 figures, 2 tables
