WSEAS Transactions on Applied and Theoretical Mechanics
Print ISSN: 1991-8747, E-ISSN: 2224-3429
Volume 9, 2014
Reactionless Motion Explained by the Laws of the Nonlinear Dynamics Leading to a New Method to Explain and Calculate the Gyroscopic Torque and its Possible Relation to the Spin of Electron
Author:
Abstract: On one hand the extant mechanics is based on the understanding that the six degrees of freedom are mutually isolated i.e. momentums and angular momentums can not “jump” from one to another degree of freedom. This is a natural consequence of the Newtonian Laws of Dynamics. But the natural example of gyroscope demonstrates that if a body rotates about axis X and turns about Y, a gyroscopic torque generates about Z in fact demonstrates that under some circumstances the degrees of freedom can be connected in system. The accepted explanation of the phenomenon by means of the method of the vector multiplication in criticized and in fact it just models the phenomenon. The Author’s experience shows that the gyroscopic torque is a result of the inertial effect of the changed direction of the orbiting masses in the plane of turning. We can determine the inertial effect of the changed direction using the Newtonian Laws of Dynamics. Then we realize that the First Newtonian Law states that speed and direction are equal in rights conserved values but on the other hand the Second and Third Newtonian Laws formulate the inertial effect of the changed speed in the frame of the given direction only. So we need to formulate parallel Laws formulating the inertial effect of the changed direction. Applying these understandings to the gyroscopic torque we formulate a new formula showing that the gyroscopic torque depends on the sine function of the correlation between the angular speeds of turning and rotation. We find that the new formula and the one of the vector multiplication calculate almost equal results if the angular speed of rotation is much bigger then the one of turning. Then we find the condition. Exploring the sine function we find that the body does not generate gyroscopic torque if the angular speed of rotation is 1/2 of the one of the turning. Possibly, it corresponds to the 1/2 spin of electron. The paper is an extended version of the already published one [1].
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Keywords: Reactionless motion, Classical mechanics, vector multiplication, gyroscopic torque, spin of electron
Pages: 252-263
WSEAS Transactions on Applied and Theoretical Mechanics, ISSN / E-ISSN: 1991-8747 / 2224-3429, Volume 9, 2014, Art. #24