Symplectic integrators and their application to dynamical astronomy     

Hiroshi Kinoshita  Haruo Yoshida  Hiroshi Nakai 《Celestial Mechanics and Dynamical Astronomy》1990,50(1):59-71

Symplectic integrators have many merits compared with traditional integrators:  相似文献   

Long-term behavior of the motion of Pluto over 5.5 billion years     

Hiroshi Kinoshita  Hiroshi Nakai 《Earth, Moon, and Planets》1996,72(1-3):165-173

The motion of Pluto is said to be chaotic in the sense that the maximum Lyapunov exponent is positive: the Lyapunov time (the inverse of the Lyapunov exponent) is about 20 million years. So far the longest integration up to now, over 845 million years (42 Lyapunov times), does not show any indication of a gross instability in the motion of Pluto. We carried out the numerical integration of Pluto over the age of the solar system (5.5 billion years ≈ 280 Lyapunov times). This integration also did not give any indication of chaotic evolution of Pluto. The divergences of Keplerian elements of a nearby trajectory at first grow linearly with the time and then start to increase exponentially. The exponential divergences stop at about 420 million years. The divergences in the semi-major axis and the mean anomaly ( equivalently the longitude and the distance) saturate. The divergences of the other four elements, the eccentricity, the inclination, the argument of perihelion, and the longitude of node still grow slowly after the stop of the exponential increase and finally saturate.  相似文献   

Nutrient status of Otsuchi Bay (northeastern Japan) following the 2011 off the Pacific coast of Tohoku Earthquake     

Hideki Fukuda  Ryosuke Katayama  Yanhui Yang  Hiroyuki Takasu  Yuichiro Nishibe  Atsushi Tsuda  Toshi Nagata 《Journal of Oceanography》2016,72(1):39-52

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