The motion of a disk rolling on a vibrating horizontal plane: Feasible control and path controllability
نویسندگان
چکیده
منابع مشابه
The Rolling Motion of a Disk on a Horizontal Plane
Recent interest in the old problem of the motion of a coin spinning on a tabletop has focused on mechanisms of dissipation of energy as the angle α of the coin to the table decreases, while the angular velocity Ω of the point of contact increases. Following a review of the general equations of motion of a thin disk rolling without slipping on a horizontal surface, we present results of simple e...
متن کاملThe rolling of a disk on a horizontal plane and Euler’s disk
The rolling of a disk (or hoop, etc.) on a horizontal plane – without dissipation – is a classical problem. Many second-year undergraduate students of the author’s generation, studied the stability of the motion in which the disk rolls steadily in a straight line. The problem is treated in the text book [1], the author used as an undergraduate 40 years ago. Current mathematical software, e.g. M...
متن کاملThe rolling of a disk on a horizontal plane: II. Euler’s disk
This paper continues the study of a disk rolling on a horizontal plane. In this Part we focus our efforts on the nonlinear oscillations about the equilibria, appropriate to modelling the later stages of the Euler disk motions, when the disk is nearly horizontal.
متن کاملSteady Motion of a Rigid Disk of Finite Thickness on a Horizontal Plane
The article discusses the steady motion of a rigid disk of finite thickness rolling on its edge on a horizontal plane under the influence of gravity. The governing equations are presented and two cases allowing for a steady state solution are considered: rolling on consistently rough ground and rolling on perfectly smooth ground. The conditions of steady motion are derived for both kinds of gro...
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ژورنال
عنوان ژورنال: Mathematical and Computer Modelling
سال: 1996
ISSN: 0895-7177
DOI: 10.1016/0895-7177(96)00001-5