Mathematical Models for Motions of a Gyroscope with One Side Support

Usubamatov, Ryspek

doi:10.1007/978-981-15-6475-8_6

Cited by 2 publications

(7 citation statements)

References 7 publications

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“…The components of the torques generated by centrifugal T ct:y and inertial T in:x forces that have the same expression are removed from Equations (2) and (3). The simplification and modification of these equations are similar to the solution presented in the manuscripts [17,18], wherein this process is justified in detail. Modified equations are presented by the following system:…”

Section: Case Studymentioning

confidence: 95%

“…The action of external load on a gyroscope generates resistance and precession torques originated by the rotation of the mass-elements of the spinning rotor. The mathematical models for the inertial torques acting on a gyroscope are presented in several publications [16][17][18][19][20]. One publication contains incorrect mathematical models for the interrelation of external and internal torques acting on a gyroscope [20].…”

Section: Methodsmentioning

confidence: 99%

“…where Equation ( 6) represents the dependency of the angular velocities of the gyroscope around axes ox and oy that were added to Equations ( 4) and ( 5). This solution is presented in manuscripts [17,18] that use similar analytical approaches. All other parameters are as specified above.…”

Section: Case Studymentioning

confidence: 99%

“…The actions of the system of inertial torques around the axes of the gyroscope are interrelated and manifest all gyroscopic properties that were previously unexplainable. Today, the physics and mathematical models of gyroscopes' inertial torques are well described and have been validated [16][17][18][19][20]. However, the new analytical approach still has some mathematical errors.…”

Section: Introductionmentioning

confidence: 99%

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Physics of Gyroscope’s “Antigravity Effect”

Usubamatov

2019

Advances in Mathematical Physics

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The physics of gyroscopic effects are more complex than presented in existing mathematical models. The effects presented by these models do not match the real forces acting on gyroscopic devices. New research in this area has demonstrated that a system of inertial torques, which are generated by the rotating mass of spinning objects, acts upon a gyroscope. The actions of the system of inertial forces are validated by practical tests of the motions of a gyroscope with one side support. The action of external load torque on a gyroscope with one side support demonstrates that the gyroscope’s upward motion is wrongly called an “antigravity” effect. The upward motion of a gyroscope is the result of precession torque around its horizontal axis. The novelty of the present work is related to the mathematical models for the upward and downward motions of gyroscopes influenced by external torque around the vertical axis. This analytical research describes the physics of gyroscopes’ upward motion and validates that gyroscopes do not possess an antigravity property.

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Section: Case Studymentioning

confidence: 95%

Section: Methodsmentioning

confidence: 99%

Section: Case Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Physics of Gyroscope’s “Antigravity Effect”

Usubamatov

2019

Advances in Mathematical Physics

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“…The modern industry widely uses MEMS (Micro-Electromechanical Systems) and optical gyroscopes as angular velocity sensors. However, mechanical gyroscopes are still used in aeronautics, navigation systems, the engineering industry, as a drive in target coordinators for self-guided missiles, as an executive organ in spacecraft control systems, and in autonomous space exploration systems [18,19]. Mechanical gyroscopes primarily consist of a rotating disc, and an axial shaft as well as frames.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solutions of the 3-DOF Gyroscope Model

Krzysztofik,

Blasiak

2024

Electronics

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The motion of a rigid body (a gyroscope) is one of the key issues in classical mechanics. It remains a significant challenge, as evidenced by its extensive practical implementations in various scientific disciplines and engineering operations. It is important to obtain analytical solutions, as they provide solutions that depend directly on the system’s parameters, which can be definitively interpreted. The coupling of numerical and analytical solutions allows for a more precise representation of the real phenomenon. The main objective of the article was to formulate analytical solutions for the motion of a Cardan suspension gyroscope subjected to controlling torque moments. Analytical solutions for the proposed mathematical model were developed using the Laplace transform and Green’s function. Subsequently, they were validated by numerical tests. The obtained analytical solutions are universally applicable, regardless of the type of controlling moments.

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Mathematical Models for Motions of a Gyroscope with One Side Support

Cited by 2 publications

References 7 publications

Physics of Gyroscope’s “Antigravity Effect”

Physics of Gyroscope’s “Antigravity Effect”

Analytical Solutions of the 3-DOF Gyroscope Model

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