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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://elar.urfu.ru/handle/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 ученых УрФУ, проиндексированные в SCOPUS и WoS CC |
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