Corrected mathematical models for inertial torques generated by a spinning sphere
- International Robotics & Automation Journal
-
Ryspek Usubamatov, Almazbek Arzybaev
Abstract
The recent publications about inertial torques acting on spinning objects describe their
physics by mathematical models. The several inertial torques are generated by the
rotating mass which produces centrifugal, Coriolis forces, and the change in the angular
momentum. The values of the inertial torques depend on the geometries of the spinning
objects. The volumetric geometries of the objects request complex analytical processing
of the expressions for the inertial torques. The analysis of the known publication related
to the spinning sphere shows the expressions of inertial torques derived from errors in the
mathematical processing of integral equations. The wrong limits of the integral equations
that give incorrect values for the inertial torques of the spinning sphere present these
errors. This manuscript presents the corrected mathematical model for the inertial torques
generated by the rotating mass of the spinning solid and hollow sphere.
Keywords
inertial torques, gyroscope theory, spinning sphere
