In this paper we analyze the dynamical behavior of large dust grains in the vicinity of a cometary nucleus. To this end we consider the gravitational field of the irregularly shaped body, as well as its electric and magnetic fields. Without considering the effect of gas friction and solar radiation, we find that there exist grains which are static relative to the cometary nucleus; the positions of these grains are the stable equilibria. There also exist grains in the stable periodic orbits close to the cometary nucleus. The grains in the stable equilibria or the stable periodic orbits won’t escape or impact on the surface of the cometary nucleus. The results are applicable for large charge dusts with small area-mass ratio which are near the cometary nucleus and far from the Solar. It is found that the resonant periodic orbit can be stable, and there exist stable non-resonant periodic orbits, stable resonant periodic orbits and unstable resonant periodic orbits in the potential field of cometary nuclei. The comet gravity force, solar gravity force, electric force, magnetic force, solar radiation pressure, as well as the gas drag force are all considered to analyze the order of magnitude of these forces acting on the grains with different parameters. Let the distance of the dust grain relative to the mass centre of the cometary nucleus, the charge and the mass of the dust grain vary, respectively, fix other parameters, we calculated the strengths of different forces. The motion of the dust grain depends on the area-mass ratio, the charge, and the distance relative to the comet’s mass center. For a large dust grain (> 1 mm) close to the cometary nucleus which has a small value of area-mass ratio, the comet gravity is the largest force acting on the dust grain. For a small dust grain (< 1 mm) close to the cometary nucleus with large value of area-mass ratio, both the solar radiation pressure and the comet gravity are two major forces. If the a small dust grain which is close to the cometary nucleus have the large value of charge, the magnetic force, the solar radiation pressure, and the electric force are all major forces. When the large dust grain is far away from the cometary nucleus, the solar gravity and solar radiation pressure are both major forces.

中文翻译：

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彗核周围尘埃运动的哈密顿公式和扰动

在本文中，我们分析了彗核附近大尘埃颗粒的动力学行为。为此，我们考虑不规则形状物体的引力场，以及它的电场和磁场。不考虑气体摩擦和太阳辐射的影响，我们发现存在相对于彗核静止的颗粒；这些晶粒的位置是稳定的平衡点。在靠近彗核的稳定周期轨道上也存在晶粒。处于稳定平衡或稳定周期轨道的晶粒不会逃逸或撞击彗核表面。该结果适用于靠近彗核、远离太阳的、面积质量比小的大电荷尘埃。发现共振周期轨道是稳定的，彗核势场中存在稳定的非共振周期轨道、稳定的共振周期轨道和不稳定的共振周期轨道。彗星重力、太阳重力、电力、磁力、太阳辐射压力以及气体拖曳力都被考虑在内，以分析这些作用在不同参数颗粒上的力的大小顺序。让尘埃颗粒相对于彗核质心的距离，尘埃颗粒的电荷和质量分别变化，固定其他参数，我们计算出不同作用力的强度。尘埃颗粒的运动取决于面积质量比、电荷以及相对于彗星质心的距离。对于较大的尘粒 (> 1 mm）靠近面积质量比值较小的彗核，彗星引力是作用在尘埃颗粒上的最大力。对于面积质量比值大的靠近彗核的小尘埃颗粒（<1mm），太阳辐射压力和彗星引力是两个主要作用力。如果靠近彗核的小尘埃颗粒电荷值大，则磁力、太阳辐射压力和电力都是主要作用力。当大尘埃颗粒远离彗核时，太阳引力和太阳辐射压力都是主要作用力。太阳辐射压力和彗星引力是两种主要的力量。如果靠近彗核的小尘埃颗粒电荷值大，则磁力、太阳辐射压力和电力都是主要作用力。当大尘埃颗粒远离彗核时，太阳引力和太阳辐射压力都是主要作用力。太阳辐射压力和彗星引力是两种主要的力量。如果靠近彗核的小尘埃颗粒电荷值大，则磁力、太阳辐射压力和电力都是主要作用力。当大尘埃颗粒远离彗核时，太阳引力和太阳辐射压力都是主要作用力。