The known publications related to the gyroscope theory consider only several geometries of the spinning rotors, like the disc, bars, rings, spheres, and others. The geometries of the spinning objects in engineering can have many designs that generate different values of inertial torques. A computing of inertial torques produced by the object’s rotating masses depends on the radii of their locations. Gyroscopic devices with a spinning torus or ring like other objects should be computed for the quality of their operation. The simplified expression for the radius of the mass disposition for the ring is presented by its middle radius which does not give the correct results for inertial torques and motions of gyroscopic devices. The radius of distributed masses of a ring is bigger than its middle radius because of the differences in the external and internal semirings. A torus is a ring whose exact expression of the radius for distributed mass should be derived for the correct solution for the inertial torques generated by the rotating mass. The precise formulas for inertial torques acting on the spinning torus enable finding its optimal size for the gyroscopic devices. This paper presents the method and derivation of mathematical models for the inertial torques produced by the spinning torus and its interrelated angular velocities about the axes of rotations that manifest gyroscopic effects.

Ryspek Usubamatov

Advances in Mathematical Physics

ADVANCES IN MATHEMATICAL PHYSICS 发表的论文旨在理解物理现象的数学基础，并通过数学方法解决物理问题。该杂志欢迎数学物理学家、理论物理学家和数学家的投稿。除了原创研究，《数学物理学进展》还发表重点评论文章，检查最新技术，确定新兴趋势，并为发展领域提出未来方向。

The papers published in Advances in Mathematical Physics aim to deepen the understanding of the mathematical foundations of physical phenomena and to solve physical problems through mathematical methods. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians. In addition to original research articles, Advances in Mathematical Physics also publishes review articles that examine the latest techniques, identify emerging trends, and propose future directions for the development of the field.

《Advances in Mathematical Physics》发表的论文旨在深入理解物理现象的数学基础，并通过数学方法解决相关的物理问题。该杂志欢迎数学物理学家、理论物理学家和数学家的投稿。除了原创研究文章外，《Advances in Mathematical Physics》还发表重点评论文章，探讨最新技术，识别新兴趋势，并为该领域的发展提出未来方向。

Category	Quartile
物理与天体物理	4
物理与天体物理, 物理数学物理	4

Gyroscopic Torques Generated by a Spinning Ring Torus

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