Relevant bibliographies by topics / Lagrange gyroscope

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Lagrange gyroscope'

Author: Grafiati
Published: 28 May 2022
Last updated: 31 July 2025

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Journal articles on the topic "Lagrange gyroscope"

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Sviatenko, Ya. "ON STABILIZATION OF UNSTABLE ROTATION IN THE RESISTING MEDIUM OF THE LAGRANGE GYROSCOPE USING THE SECOND GYROSCOPE AND ELASTIC HINGES." Mechanics And Mathematical Methods 3, no. 2 (2021): 103–16. http://dx.doi.org/10.31650/2618-0650-2021-3-2-103-116.

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The possibility of stabilizing an unstable uniform rotation in a resisting medium of a "sleeping" Lagrange gyroscope using a rotating second gyroscope and elastic spherical hinges is considered. The "sleeping" gyroscope rotates around a fixed point with an elastic recovery spherical hinge, and the second gyroscope is located above it. The gyroscopes are also connected by an elastic spherical restorative hinge and their rotation is supported by constant moments directed along their axes of rotation. It is shown that stabilization will be impossible in the absence of elasticity in the common joi
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Kononov, Yurii, and Yaroslav Sviatenko. "On the subject of influence of dissipative and constant of moments on the stability of uniform rotations of non-free two elastically connected gyroscopes of Lagrange." Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine 34 (April 24, 2021): 50–61. http://dx.doi.org/10.37069/1683-4720-2020-34-6.

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The conditions for asymptotic stability of uniform rotations in a resisting medium of two heavy Lagrange gyroscopes connected by an elastic spherical hinge are obtained in the form of a system of three inequalities. The bottom gyroscope has a fixed point. The rotation of the gyroscopes is maintained by constant moments in the inertial coordinate system. The influence of the elasticity of the hinge on the stability conditions is estimated. It is shown that for a sufficiently high rigidity of the hinge, the asymptotic stability conditions are determined by only one inequality, which coincides wi
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Kononov, Yuri, and Yaroslav Sviatenko. "On the subject of influence of dissipative and permanent momentums on stability of uniform rotations of two elastically connected free gyroscopes of Lagrange." Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine 33 (December 27, 2019): 132–41. http://dx.doi.org/10.37069/1683-4720-2019-33-11.

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In many works, there are studies of the asymptotic stability of rotation of a free Lagrange gyroscope in a resisting medium. This article generalizes this problem to the case of uniform rotations of two free Lagrange gyroscopes connected by an elastic restoring spherical hinge. The rotation of each gyroscope is maintained by a constant moment in an inertial coordinate system. The characteristic equation of the perturbed motion is presented in the form of an algebraic equation of the fourth degree with complex coefficients. Based on the innor approach, conditions of asymptotic stability are obt
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Saypulaev, M. R., I. V. Merkuryev, A. V. Solovyev, and A. N. Tarasov. "Study on free oscillations of a micromechanical gyroscope taking into account the nonorthogonality of the torsion axes." Advanced Engineering Research 21, no. 3 (2021): 231–38. http://dx.doi.org/10.23947/2687-1653-2021-21-3-231-238.

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Introduction. The paper is devoted to the study on free oscillations of the sensing element of a micromechanical R-Rtype gyroscope of frame construction developed by the Kuznetsov Research Institute of Applied Mechanics, taking into account the nonorthogonality of the torsion axes. The influence of the instrumental manufacturing error on the accuracy of a gyroscope on a movable base in the case of free oscillations is studied. The work objective was to improve the device accuracy through developing a mathematical model of an R-R type micromechanical gyroscope, taking into account the nonorthog
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Yang, Haotian, Bin Zhou, Lixin Wang, Haifeng Xing, and Rong Zhang. "A Novel Tri-Axial MEMS Gyroscope Calibration Method over a Full Temperature Range." Sensors 18, no. 9 (2018): 3004. http://dx.doi.org/10.3390/s18093004.

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The micro-electro-mechanical inertial measurement unit (MEMS-IMU) has gradually become a research hotspot in the field of mid-low navigation, because of its advantages of low cost, small size, light weight, and low power consumption (CSWap). However, the performance of MEMS-IMUs can be severely degraded when subjected to temperature changes, especially gyroscopes. In order to make full use of the navigation accuracy, this paper proposes an optimized error calibration method for a tri-axial MEMS gyroscope across a full temperature range. First of all, a calibration error model is established wh
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Leshchenko, D., and T. Kozachenko. "PROBLEMS OF EVOLUTION OF RIGID BODY MOTION SIMILAR TO LAGRANGE TOP." Mechanics And Mathematical Methods 4, no. 1 (2022): 23–31. http://dx.doi.org/10.31650/2618-0650-2022-4-1-23-31.

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The problem of evolution of the rigid body rotations about a fixed point continues to attract the attention of researches. In many cases, the motion in the Lagrange case can be regarded as a generating motion of the rigid body. In this case the body is assumed to have a fixed point and to be in the gravitational field, with the center of mass of the body and the fixed point both lying on the dynamic symmetry axes of the body. A restoring torque, analogues to the moment of the gravity forces, is created by the aerodynamic forces acting on the body in the gas flow. Therefore, the motions, close
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Kononov, Yu. "ON THE STABILITY OF ROTATION OF A FREE SYSTEM OF TWO ELASTICLY CONNECTED RIGID BODIES." Mechanics And Mathematical Methods 5, no. 2 (2023): 6–15. http://dx.doi.org/10.31650/2618-0650-2023-5-2-6-15.

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The equations of rotation of the free system of two rigid bodies connected by an elastic spherical joint or a Hook joint are derived. Assuming that the center of mass of the rigid bodies is located on the third main axis of inertia, the equations of the disturbed motion of the mechanical system under consideration are written in the form of eight ordinary differential equations with periodic coefficients. In the case of two Lagrangian gyroscopes, a characteristic equation of the fourth order is obtained. On the basis of the Lénar-Schipar criterion, written in innor form, the necessary conditio
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Kholostova, O. V. "A case of periodic motion for a Lagrange gyroscope with a vibrating suspension." Doklady Physics 45, no. 12 (2000): 690–93. http://dx.doi.org/10.1134/1.1342451.

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Lavasani, Reza Esbati, and Amirali Nikkhah. "Analyzing and Control of Drive Mode in a Vibratory Ring Gyroscope." Applied Mechanics and Materials 390 (August 2013): 414–18. http://dx.doi.org/10.4028/www.scientific.net/amm.390.414.

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One of the challenges in MEMS era is dynamical modeling and control. This paper presents the analysis and control of drive mode of an 80 mm-thick, 1.1 mm in diameter high aspect-ratio (20:1) ring vibratory MEMS gyro. At first dynamic model of MEMS is derived through energy and Lagrange equations. Then state space equation is derived. Natural frequencies were derived by ABAQUS software and through equations. Frequency analysis was applied to analyze system and making comparison between two applied approaches in deriving frequencies. At last modified PID control was designed based on previous se
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Huo, Yan, Shunqing Ren, Zhennan Wei, and Guoxing Yi. "Standing Wave Binding of Hemispherical Resonator Containing First–Third Harmonics of Mass Imperfection under Linear Vibration Excitation." Sensors 20, no. 19 (2020): 5454. http://dx.doi.org/10.3390/s20195454.

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Due to complicated processing technology, the mass distribution of a hemispherical resonator made of fused silica is not uniform, which can affect the azimuth of the standing wave of a resonator under the linear vibration excitation. Therefore, the analysis of standing wave evolution of a resonator with mass imperfection under linear vibration excitation is of significance for the improvement of the output accuracy of a gyroscope. In this paper, it is assumed that the resonator containing the first–third harmonics of mass imperfection is excited by horizontal and vertical linear vibration, res
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Dissertations / Theses on the topic "Lagrange gyroscope"

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Акуленко, Л. Д., Д. Д. Лещенко та Т. А. Козаченко. "Движения твердого тела, близкие к случаю Лагранжа". Thesis, Сумский государственный университет, 2017. http://essuir.sumdu.edu.ua/handle/123456789/65372.

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В работе исследуется возмущенное движение относительно неподвижной точки динамически симметричного тяжелого твердого тела под действием момента сил произвольной природы. Момент силы тяжести не рассматривается как возмущающий момент, а относится к невозмущенному движению, которое представляет собой движение в случае Лагранжа.
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Book chapters on the topic "Lagrange gyroscope"

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Brunner, Johannes, Nis Keilhauer, Vincent Vellguth, Heide Brandtstädter, and Horst Schulte. "Nonlinear Modeling and Control of 3-DOF Gyroscope Actuated Furuta Pendulum by Takagi-Sugeno Fuzzy Systems." In Proceedings - 33. Workshop Computational Intelligence: Berlin, 23. – 24. November 2023. KIT Scientific Publishing, 2023. http://dx.doi.org/10.58895/ksp/1000162754-7.

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This paper presents the derivation of the equations of motion of a 3-DOF gyroscope with a pendulum attachment through the Euler-Lagrange approach, followed by a conversion into a Takagi-Sugeno Fuzzy Model. First, suitable coordinate frames and generalized coordinates are defined, followed by the definition of the kinetic energy of each body frame of the gyroscope. Next, the kinetic and potential energy of the pendulum attachment is described. The derived equations of motion are then validated by simulation and compared to the behavior of a testbed system (see Figure 1). The conversion to the T
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Conference papers on the topic "Lagrange gyroscope"

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Permadi, Yayang, Adytia Darmawan, and Endra Pitowarno. "Application of Lagrange Method to Analyze Forces of Gyroscope Inverted Pendulum." In 2019 International Electronics Symposium (IES). IEEE, 2019. http://dx.doi.org/10.1109/elecsym.2019.8901522.

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Chebanov, Dmitriy, and Jose A. Salas. "On Permanent Rotations of a System of Two Coupled Gyrostats in a Central Newtonian Force Field." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-47434.

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This paper studies the problem of the motion of a chain of two gyrostats coupled by an ideal spherical joint. The chain moves about a fixed point in a central Newtonian force field. Under the assumption that the gyrostatic moment of each gyrostat is constant relative to its carrier, the paper establishes and analyzes the conditions for existence of the chain’s permanent rotations about a vertical axis. For a case when each gyrostat has the mass distribution analogous to the one of a Lagrange gyroscope, the paper derives and analyzes the necessary conditions for stability of the permanent rotat
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Marzban, Mostapha, and Aria Alasty. "Dynamic Analysis of an Amphibious Single Wheel Robot, Part 1: Moving in Straight Path." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35876.

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A single wheel, gyroscopically stabilized robot is a sharp-edged wheel actuated by a spinning flywheel for steering and a drive motor for propulsion. The spinning flywheel acts as a gyroscope to stabilize the robot and it can be tilted to achieve steering. In this paper first the kinematics of a single wheel robot, like Gyrover, in water is considered and then a simple mechanism for its movement in water is proposed. After hydrodynamic analysis of the robot a complete dynamics model is designed with Lagrange energy method. The only simplification used here is neglecting the added mass effect i
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Marzban, Mostapha, and Dina Alizadeh. "Positioning and Tracking Control of an Amphibious Single Wheel Robot." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-66281.

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Amphibious single wheel robot consists of a sharp-edged wheel actuated by a spinning flywheel for steering and a drive motor for propulsion. The spinning flywheel acts as a gyroscope to stabilize the robot and also can be tilted to achieve steering. In this paper, the kinematics of a single wheel robot in water, Gyrover, is analyzed and then a simple mechanism for driving it is proposed. In previous studies, Lagrange approach is used for hydrodynamic modeling of the robot. A nonlinear position controller is designed to bring the robot to any desired position. Based on the designed controller,
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Marzban, Mostapha, and Aria Alasty. "Stability Control of an Amphibious Single Wheel Robot." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-44020.

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Single wheel robots are typically those kinds of robots which contain all the necessary mechanizations, namely the stabilization and driving mechanizations, within a shell-liked housing appearing analogous to a wheel. These robots have proved to be useful in various fields of industry due to their advantages of giving high instant acceleration and maintaining high cruise speeds for considerable amount of time in addition to being compact and small. It is a sharp-edged wheel actuated by a spinning flywheel for steering and a drive motor for propulsion. The spinning flywheel acts as a gyroscope
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Murakami, Hidenori, and Takeyuki Ono. "Analysis and Design of Twin Gyroscopes for Ocean-Wave Energy Converters and Ship Roll-Stabilizers." In ASME 2019 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/imece2019-11435.

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Abstract Twin-gyroscopic systems are designed for ocean-wave energy converters and ship roll-stabilizers to double desirable gyroscopic effects and eliminate undesirable reaction torques. In deriving analytical equations of motion, the configuration spaces of gyroscopic systems are defined by using body-attached moving frames. The moving frame of each constituent body is defined by its inertial coordinates of the center of mass and a rotation matrix which expresses the attitude of its coordinate axes from the inertial coordinate axes. Therefore, to utilize powerful Lagrange’s method, it is ext
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Zirkelback, Nicole L., and Jerry H. Ginsberg. "Ritz Series Analysis of Rotating Machinery Incorporating Timoshenko Beam Theory." In ASME Turbo Expo 2001: Power for Land, Sea, and Air. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/2001-gt-0244.

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A shaft with attached rigid disks is modeled as a rotating Timoshenko beam supported by general compliant, nonconservative bearing supports. The continuous shaft-disk system is described with kinetic and potential energy functionals that fully account for transverse shear, translational and rotatory inertia, and gyroscopic coupling. Ritz series expansions are used to describe the flexural displacements and cross-sectional rotations about orthogonal fixed axes. The equations of motion are derived from Lagrange’s equations and placed in a state-space form that preserves the skew-symmetric gyrosc
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Khulief, Y. A., S. Bashmal, and F. A. Al-Sulaiman. "Coupled Torsional Vibrations in Drilling Systems." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-80489.

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The contact between the drilling bit and formation is known to excite severe torsional and axial vibrations in the drillstring. A dynamic model of the drillstring including both drillpipe and drillcollars is formulated. The equation of motion of the rotating drillstring is derived using Lagrangean approach together with the finite element method. The model accounts for the gyroscopic effect, the torsional/bending inertia coupling, the axial/bending geometric nonlinear coupling, and the stiffening effect due to the gravitational force field. Reduced order modal form of the dynamic equations is
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Canfield, Stephen L., R. Randall Soper, and Charles F. Reinholtz. "Dynamic Force Analysis of the Carpal Wrist." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/dac-3970.

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Abstract The Carpal Wrist is a novel, parallel-architecture device that exhibits many features desirable in a robotic wrist. Previous static analysis has verified the large, singularity-free workspace and the excellent force-bearing ability of the Carpal Wrist. Here, the parallel structure is shown to be particularly advantageous when considered dynamically due to its lightweight structure and multiple load bearing members. The dynamic equations of motion are derived in closed form by direct application of Lagrange’s equations to the kinematic model. The model assumes a relatively massive tool
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Shen, I. Y., and Hyunchul Kim. "Vibration Analysis of Rotating Asymmetric Structures." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84036.

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This paper is to develop a unified algorithm to analyze vibration of spinning asymmetric rotors with arbitrary geometry and complexity. As a first approximation, the effects of housings and bearings are not included in this analysis. The unified algorithm consists of three steps. The first step is to conduct a finite element analysis on the corresponding stationary rotor to extract natural frequencies and mode shapes. The second step is to represent the vibration of the spinning rotor in terms of the mode shapes and their modal response in a coordinate system that is rotating with the spinning
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