 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4810 |
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| << Previous article | Volume 58, Issue 8 / 2023 | Next article >> |
| A.G. Petrov, "On Kinematic Description of the Motion of a Rigid Body," Mech. Solids. 58 (8), 2723-2730 (2023) |
| Year |
2023 |
Volume |
58 |
Number |
8 |
Pages |
2723-2730 |
| DOI |
10.3103/S0025654423080150 |
| Title |
On Kinematic Description of the Motion of a Rigid Body |
| Author(s) |
A.G. Petrov (Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, 119526 Russia, petrovipmech@gmail.com) |
| Abstract |
A system of ordinary differential equations has been derived for a vector of finite rotation
corresponding to Euler’s theorem: the vector of finite rotation is directed along the axis of finite rotation of a solid, and its length is equal to the angle of plane rotation around this axis. The system of
equations is explicitly resolved with respect to the time derivative of the rotation vector components.
The right part of the system depends on the rotation vector and the angular velocity vector in the principle axes. The obtained system of equations is shown to be equivalent to the system of equations for
quaternions. The coordinates of the orts of the principle axes of a rigid body in fixed axes are expressed
in terms of finite rotation angles and the components of angular velocity using simple analytical formulas. |
| Keywords |
Euler’s theorem on finite rotation, rigid body kinematics, quaternion, orientation |
| Received |
21 February 2023 | Revised |
19 June 2023 | Accepted |
15 July 2023 |
| Link to Fulltext |
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