Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/102428
Title: Construction of a programmed trajectory in the configuration space of rotations for solving the problem of the solid rotation
Authors: Mityushov, E. A.
Misyura, N. E.
Lamotkin, A. E.
Issue Date: 2020
Publisher: IOP Publishing Ltd
Citation: Mityushov E. A. Construction of a programmed trajectory in the configuration space of rotations for solving the problem of the solid rotation / E. A. Mityushov, N. E. Misyura, A. E. Lamotkin. — DOI 10.1088/1742-6596/1705/1/012031 // Journal of Physics: Conference Series. — 2020. — Vol. 1705. — Iss. 1. — 012031.
Abstract: The paper proposes method of programmed control based on the concept of solving the inverse dynamic problem. As a configurational space of rotations, it is proposed to consider a sphere with a radius of 2 π in the three-dimensional Euclidean space, which is the image of the unit Sp(1) quaternions. A linear relationship has been established between the angular velocity vector of a solid in its spherical motion and the velocity of a point in a sphere allowing to relate the rotation of a solid to the motion of a point inside a three-dimensional sphere. This approach allows to clearly interpret the spherical motion of a solid by the movement of a point inside this sphere, which is used by the authors to describe the rotation of a solid at arbitrary given boundary conditions for angular positions, velocities and accelerations. An example of a smooth turn from one position to another in the case when the turn is set in the sphere in the form of a polynomial of the fifth degree is given. © Published under licence by IOP Publishing Ltd.
Keywords: ROTATION
SPHERES
ANGULAR POSITIONS
CONFIGURATION SPACE
CONFIGURATIONAL SPACES
EUCLIDEAN SPACES
INVERSE DYNAMICS
LINEAR RELATIONSHIPS
PROGRAMMED CONTROLS
SPHERICAL MOTION
INVERSE PROBLEMS
URI: http://hdl.handle.net/10995/102428
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85098551646
PURE ID: 20377747
68a7d871-c564-4982-864e-436c761f0e38
ISSN: 17426588
DOI: 10.1088/1742-6596/1705/1/012031
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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