On Kinematic Description of the Motion of a Rigid Body

被引:0
作者
Petrov, A. G. [1 ]
机构
[1] Russian Acad Sci, Ishlinsky Inst Problems Mech, Moscow 119526, Russia
关键词
Euler's theorem on finite rotation; rigid body kinematics; quaternion; orientation;
D O I
10.3103/S0025654423080150
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
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.
引用
收藏
页码:2723 / 2730
页数:8
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