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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.
|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.|
|Appears in Collections:||Научные публикации, проиндексированные в SCOPUS и WoS CC|
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