Open AccessOn a property of curves given by the determining equations
Author(s) -
G. G. Bilchenko
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1479/1/012018
Subject(s) - plane (geometry) , intersection (aeronautics) , trajectory , motion (physics) , differential equation , point (geometry) , horizontal plane , channel (broadcasting) , equations of motion , mathematical analysis , mathematics , linear motion , physics , mechanics , geometry , classical mechanics , computer science , engineering , computer network , astronomy , aerospace engineering
The motion of a mechanical system consisting of a carrier and a load is considered. The carrier, located all the time in a horizontal plane, can move translationally along a rectilinear trajectory. The carrier has a rectilinear channel through which the load can move. The load is considered further on as a material point. The load can move in the channel according to a predetermined motion law. The channel axis is located in a vertical plane passing through the trajectory of the carrier. The Coulomb dry friction model is applied for simulation the forces of resistance to the motion of the carrier from the side of the underlying plane. In the conditions of the carrier motion along horizontal plane without detachment, the carrier motion differential equations are a system of three linear second-order differential equations. The influence of the system parameters on the motion of the carrier from the rest state is studied in the point of view of determining functions. An important property of the determining expressions is proved: the existence of a single intersection point of the curves given by the determining equations, which corresponds to the zero angle of setting of the channel along which the load moves.