Abstract The impact of nonspherical bodies is complex, even at low velocities where contacting bodies are assumed to be rigid. Models of varying complexity (e.g. finite element methods) can be used to evaluate such impacts, but it is advantageous to use impulsive models such as that by Stronge, which are computationally inexpensive and governed by (fixed) material interaction coefficients. Stronge’s model parameterizes nonspherical rigid-body impacts with energetic restitution and Coulomb friction coefficients. This model was successfully used in large-scale simulations of ballistic lander deployment to asteroids and comets, whose trajectories involve dozens of chaotic bounces. To better understand the complex dynamics of these bouncing trajectories, this paper performs a dedicated study of idealized bouncing in two dimensions and on a flat plane, in order to limit the involved degrees of freedom. Using a numerical implementation of Stronge’s model, the motion of a bouncing square is simulated with different impact conditions: the square’s impact attitude, velocity, and mass distribution as well as the surface restitution and friction coefficients. The simulation results are used to investigate how these conditions affect the bouncing motion of the square, with a distinction between first impacts with zero angular velocity and successive impacts in which the square is spinning. This reveals how a single ”macroscopic” bounce that separates two ballistic arcs may often consist of multiple micro-impacts that occur in quick succession. For the different impact conditions, we show how the number of micro-impacts per macro-bounce varies, as well as the normal, tangential, and total kinematic restitution coefficients. These are different from the energetic material restitution coefficient that parameterizes the impact. Finally, we examine how the settling time and distance of the bouncing trajectories change. These trends provide insight into the bouncing motion of ballistic lander spacecraft in small-body microgravity.

中文翻译：

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恢复、摩擦和姿态对二维低速刚体冲击的影响

摘要 非球形物体的影响是复杂的，即使在假设接触物体是刚性的低速下也是如此。可以使用不同复杂性的模型（例如有限元方法）来评估这种影响，但使用诸如 Stronge 的脉冲模型是有利的，这些模型计算成本低且受（固定）材料相互作用系数控制。Stronge 的模型使用能量恢复和库仑摩擦系数对非球形刚体冲击进行参数化。该模型已成功用于对小行星和彗星的弹道着陆器部署进行大规模模拟，这些小行星和彗星的轨迹涉及数十次混沌弹跳。为了更好地理解这些弹跳轨迹的复杂动力学，本文对二维平面上的理想化弹跳进行了专门研究，以限制所涉及的自由度。使用Stronge 模型的数值实现，在不同冲击条件下模拟弹跳方块的运动：方块的冲击姿态、速度和质量分布以及表面恢复和摩擦系数。模拟结果用于研究这些条件如何影响方块的弹跳运动，区分零角速度的第一次撞击和方块旋转的连续撞击。这揭示了分隔两个弹道弧的单个“宏观”反弹如何通常由快速连续发生的多个微观影响组成。对于不同的冲击条件，我们展示了每次宏观反弹的微冲击数量如何变化，以及法线、切线、和总运动恢复系数。这些不同于将影响参数化的高能材料恢复系数。最后，我们研究了弹跳轨迹的稳定时间和距离如何变化。这些趋势提供了对弹道着陆器航天器在小体微重力下的弹跳运动的洞察。