Abstract
The properties and characteristics of torque free gyros with rotational symmetry and changing moments of inertia are the subject of the subsequent discussion. It shall be understood that the symmetry can be expressed by the notation (A=B) which does not presuppose geometric symmetry, where A and B are the principle moments of inertia about x and y axes respectively. We study the case of a torque free gyro upon which no external torque is acting. The equations of motion are derived when the origin of the xyz-coordinate system coincides with the gyro’s mass center c. This study is useful for the satellites, which have rotational symmetry and changed inertia moments, the antennas and the solar power collector systems.
Highlights
A gyro is a body of rotation which is set spinning at a large angular velocity around its axis of symmetry
The properties and characteristics of torque free gyros with rotational symmetry and changing moments of inertia are the subject of the subsequent discussion
It shall be understood that the symmetry can be expressed by the notation ( A = B) which does not presuppose geometric symmetry, where A and B are the principle moments of inertia about x and y axes respectively
Summary
A gyro is a body of rotation which is set spinning at a large angular velocity around its axis of symmetry. Other textbooks [3] [4] treat the problem of torque-induced precession of a top based on Euler equations, which are referred to the non-inertial reference frame rotating together. The problem of the torque free inertial rotation of a symmetrical top is discussed, in particular, in [5] and illustrated by a simulation computer program (free rotation of an axially symmetrical body) [6]. We consider a gyro body with xyz-coordinate system fixed of it, such that the z-axis of the body is the axis of symmetry and the inertia tensor is assumed to take the form. Where i, ˆj and kare the unit vectors in the x, y and z directions
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