Open AccessConstruction of a programmed trajectory in the configuration space of rotations for solving the problem of the solid rotation
Author(s) -
E. A. Mityushov,
N. E. Misyura,
A. E. Lamotkin
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 - 10.1088/1742-6596/1705/1/012031
Subject(s) - quaternion , rotation (mathematics) , unit sphere , euclidean space , angular velocity , mathematics , position (finance) , mathematical analysis , point (geometry) , solid body , boundary (topology) , motion (physics) , rigid body , polynomial , rotation matrix , circular motion , radius , rotation around a fixed axis , geometry , classical mechanics , physics , computer science , computer security , finance , acoustics , economics
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.