Effects of restitution, friction, and attitude on 2D low-velocity rigid-body impacts

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.