Abstract
The motion of a solid in a homogeneous gravity field under inelastic collisions with an immovable absolutely smooth horizontal plane is considered. The body is a homogeneous ellipsoid of revolution. There exists a motion in which the ellipsoid symmetry axis is directed along a fixed vertical, the ellipsoid itself rotates about this axis at a constant angular velocity, and the ellipsoid bounce height over the plane decreases from impact to impact because of the collisions. We study the motion of the ellipsoid in a small neighborhood of the motion corresponding to this infinite-impact process.
The main goal is to compute the angle between the ellipsoid symmetry axis and the vertical at the discrete time instants corresponding to the collisions. The problem is solved in the first (linear) approximation. The analysis is based on the canonical transformation method used earlier in [1] to solve problems with absolutely elastic collisions.
There are quite a few studies dealing with infinite-impact processes (e.g., see the monographs [2, 3]). A method for continuous representation of systems with inelastic collisions was proposed in [4] and efficiently used in [3–5] when analyzing specific mechanical systems.
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References
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Original Russian Text © A.P. Markeev, 2013, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2013, No. 6, pp. 3–14.
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Markeev, A.P. On the evolution of rotation of a solid under inelastic collisions with a plane. Mech. Solids 48, 603–612 (2013). https://doi.org/10.3103/S0025654413060010
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DOI: https://doi.org/10.3103/S0025654413060010