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Journal articles on the topic 'Lagrange gyroscope'

Author: Grafiati

Published: 28 May 2022

Last updated: 31 July 2025

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Kononov, Yuriy, Olga Nesmelova, and Yaroslav Svyatenko. "On the stability of rotation in an environment with resistance of a suspended Lagrange gyroscope taking into account the elasticity of spherical joints." Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine 38 (June 27, 2024): 33–43. http://dx.doi.org/10.37069/1683-4720-2024-38-4.

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Based on the known equations of P.V. Kharlamov, the problem of stability of uniform rotations in a medium with resistance of a Lagrangian gyroscope on a suspension is considered, taking into account the elasticity of spherical joints, mass and inertial characteristics of the suspension and constant moments in inertial and non-inertial reference systems. The conditions of asymptotic stability of uniform rotations were obtained and analytical studies of the influence of the elasticity of hinges, mass and inertial characteristics of the suspension on the conditions of stability were carried out.

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12

Ma, Zhipeng, Xiaoli Chen, Xiaojun Jin, Yiming Jin, Xudong Zheng, and Zhonghe Jin. "Effects of Structural Dimension Variation on the Vibration of MEMS Ring-Based Gyroscopes." Micromachines 12, no. 12 (2021): 1483. http://dx.doi.org/10.3390/mi12121483.

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This study investigated the effects of structural dimension variation arising from fabrication imperfections or active structural design on the vibration characteristics of a (100) single crystal silicon (SCS) ring-based Coriolis vibratory gyroscope. A mathematical model considering the geometrical irregularities and the anisotropy of Young’s modulus was developed via Lagrange’s equations for simulating the dynamical behavior of an imperfect ring-based gyroscope. The dynamical analyses are focused on the effects on the frequency split between two vibration modes of interest as well as the rota

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13

Storozhenko, V. A. "Dissipation in systems of coupled Lagrange gyroscopes." International Applied Mechanics 40, no. 11 (2004): 1297–303. http://dx.doi.org/10.1007/s10778-005-0037-0.

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14

Wu Hui-Bin and Mei Feng-Xiang. "Symmetries of Lagrange system subjected to gyroscopic forces." Acta Physica Sinica 54, no. 6 (2005): 2474. http://dx.doi.org/10.7498/aps.54.2474.

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15

Kononov, Yuriy. "On the stability of rotation in an environment with resistance of a free system of two elastically connected rigid bodies." Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine 37 (January 23, 2024): 75–84. http://dx.doi.org/10.37069/1683-4720-2023-37-7.

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The equations of rotation in a medium with resistance of a free system of two rigid bodies connected by an elastic spherical joint or Hooke's joint are obtained. Under the assumption that the center of mass of solid bodies is located on the third axis of inertia, equations of perturbed motion are obtained. These equations are represented as eight ordinary differential equations with periodic coefficients. For two Lagrange gyroscopes, a fourth-order characteristic equation is obtained. Based on the Liénard-Schipart criterion, written in the form of innors, conditions for the asymptotic stabilit

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16

Kravets, V. V. "THE ALGORITHM FOR DETERMINING GYROSCOPIC FORCES AND MOMENTS IN THE INTERACTION WHEEL SET SPEED OF THE CARRIAGE AND RAIL." Science and Transport Progress, no. 8 (September 25, 2005): 58–60. http://dx.doi.org/10.15802/stp2005/20113.

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The algorithm of an estimation of gyroscopic forces and moments arising at interaction of wheel pair of the highspeed car and a rail is offered. The algorithm is based on application of the nonlinear differential equations of spatial movement in the form Euler-Lagrange and experimental information about kinematics parameters of movement of wheel pair formed by nonplatform inertial system.

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17

Cheng, Wei, Shunqing Ren, Boqi Xi, Zhen Tian, Youhuan Ning, and Yan Huo. "The Influence of Nonlinear High-Intensity Dynamic Processes on the Standing Wave Precession of a Non-Ideal Hemispherical Resonator." Sensors 24, no. 9 (2024): 2709. http://dx.doi.org/10.3390/s24092709.

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The properties of small size, low noise, high performance and no wear-out have made the hemispherical resonator gyroscope a good choice for high-value space missions. To enhance the precision of the hemispherical resonator gyroscope for use in tasks with large angular velocities and angular accelerations, this paper investigates the standing wave precession of a non-ideal hemispherical resonator under nonlinear high-intensity dynamic conditions. Based on the thin shell theory of elasticity, a dynamic model of a hemispherical resonator is established by using Lagrange’s second kind equation. Th

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18

Kosov, Alexander A., and Eduard I. Semenov. "On the Movement of Gyrostat under the Action of Potential and Gyroscopic Forces." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 24, no. 1 (2022): 66–75. http://dx.doi.org/10.15507/2079-6900.24.202201.66-75.

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A system of differential equations is considered that describes the motion of a gyrostat under the action of the moment of potential, gyroscopic and circular-gyroscopic forces. The form of the moment of forces is indicated for which the system has the three first integrals of a given form. An analog of V.I. Zubov’s theorem for representing solutions of gyrostat equations by power series is given, and the possibility of using this approach to predict motions is shown. For an analogue of the Lagrange case, integration in quadratures is performed. Analogues of the case of full dynamical symmetry

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19

Kononov, Yu. "On the stability of the rotation of the free system of two elastic Lagrange gyroscopes, one of which has an ideal liquid." Mechanics And Mathematical Methods 6, no. 2 (2024): 6–17. http://dx.doi.org/10.31650/2618-0650-2024-6-2-6-17.

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On the basis of the known equations of motion of the system of coupled gyrostats by P. V. Kharlamov and the state function by S. L. Sobolev, the equations of rotation of a free system of two elastically coupled Lagrange gyroscopes were derived, one of which has an arbitrary axisymmetric cavity completely filled with an ideal incompressible fluid. The rigid bodies are connected by an elastic restoring spherical hinge. A transcendental characteristic equation of the perturbed uniform rotation of the mechanical system under consideration is derived. Taking into account the fundamental tone of the

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20

Polekhin, Ivan. "Remarks on the Covering of the Possible Motion Area by Solutions in Rigid Body Systems." International Journal of Nonlinear Sciences and Numerical Simulation 20, no. 3-4 (2019): 293–302. http://dx.doi.org/10.1515/ijnsns-2018-0037.

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AbstractThe problem of motion of a rigid body with a fixed point is considered. We study qualitatively the solutions of the system after Routh reduction. For the Lagrange integrable case, we show that the trajectories of solutions starting at the boundary of a possible motion area can both cover and not cover the entire possible motion area. It distinguishes these systems from the systems without gyroscopic forces, where the trajectories always cover the possible motion area. We also present some numerical and analytical results on the same matter for the Kovalevskaya case.

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21

Shen, X. Y., J. H. Jia, M. Zhao, and J. P. Jing. "Coupled torsional-lateral vibration of the unbalanced rotor system with external excitations." Journal of Strain Analysis for Engineering Design 42, no. 6 (2007): 423–31. http://dx.doi.org/10.1243/03093247jsa304.

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The coupled torsional-lateral model of the rotor system is set up and governing equations are derived using the Lagrange approach with six degrees of freedom. The gyroscopic effect and gravity are included. Two kinds of unbalance, namely static unbalance and dynamic unbalance, are considered in the rotor system. Torsional and lateral motions are subjected to external excitations. Through numerical simulation, the developed model is used and the coupled torsional-lateral vibrations of the unbalanced rotor system under external excitations are investigated. Some new phenomena are found and discu

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22

Yu, S. D., and F. Xi. "Free Vibration Analysis of Planar Flexible Mechanisms." Journal of Mechanical Design 125, no. 4 (2003): 764–72. http://dx.doi.org/10.1115/1.1626130.

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This paper presents a methodology for accurate free vibration analysis of planar flexible mechanisms. Each flexible body is considered as a beam and modelled using higher-order beam elements for longitudinal and flexural deformations. The global equations of motion for a mechanism consisting of multiple flexible bodies are formulated using the augmented Lagrange equations. Free vibration analyses are conducted at desired fast Fourier configurations to determine instantaneous structural natural frequencies and structural mode shapes. Dynamical frequencies and dynamical mode shapes incorporating

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23

Chantarachit, Surachat. "Design and simulate of LQR-Fuzzy controller for unicycle robot with double flywheels." MATEC Web of Conferences 192 (2018): 02001. http://dx.doi.org/10.1051/matecconf/201819202001.

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This research is focus on design and simulate unicycle robot with double flywheels model with LQR-Fuzzy controller. Roll balancing torque is generated by gyroscopic effect. Pitch balancing torque is applied by inverted pendulum concept. To control the heading of the robot, the angular momentum from both flywheel is applied to control this. The robot model is based on Euler-Lagrange equations. The non-linear model is linearization by Taylor series expansion. The simulation results conducted by MATLAB/Simulink. LQR-Fuzzy is combination algorithm between LQR and Fuzzy controller. The main structu

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24

Yıldız, Hüseyin Alpaslan, and Leyla Gören-Sümer. "Stabilization of a class of underactuated Euler Lagrange system using an approximate model." Transactions of the Institute of Measurement and Control 44, no. 8 (2021): 1569–78. http://dx.doi.org/10.1177/01423312211058556.

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The energy shaping method, Controlled Lagrangian, is a well-known approach to stabilize the underactuated Euler Lagrange (EL) systems. In this approach, to construct a control rule, some nonlinear and nonhomogeneous partial differential equations (PDEs), which are called matching conditions, must be solved. In this paper, a method is proposed to obtain an approximate solution of these matching conditions for a class of underactuated EL systems. To develop this method, the potential energy matching condition is transformed to a set of linear PDEs using an approximation of inertia matrices. Henc

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25

Velasco-Herrera, Graciela. "Dynamical Properties of a System of Heavy Lagrange Gyroscopes Formed in Closed Chain Applied in a Parallel System." Advanced Materials Research 452-453 (January 2012): 507–10. http://dx.doi.org/10.4028/scientific5/amr.452-453.507.

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26

Velasco-Herrera, Graciela. "Dynamical Properties of a System of Heavy Lagrange Gyroscopes Formed in Closed Chain Applied in a Parallel System." Advanced Materials Research 452-453 (January 2012): 507–10. http://dx.doi.org/10.4028/www.scientific.net/amr.452-453.507.

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One of the most important stages in the analysis of any mechanical model is to establish and find the solution of dynamical equations. Analytical Mechanics has developed a wide range of methods for obtaining equations of motion of coupled rigid body systems that represent a mechanical model. How to use the principles of the mechanics of setting up dynamic equations leads to different forms of presentation. This circumstance is often used to obtain a special form of the equation, which simplifies the study of the dynamic properties of interest to the mechanical model. In this paper we use the m

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27

Amer, T. S., and I. M. Abady. "On the motion of a gyro in the presence of a Newtonian force field and applied moments." Mathematics and Mechanics of Solids 23, no. 9 (2017): 1263–73. http://dx.doi.org/10.1177/1081286517716734.

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This work focuses on the motion of a dynamical model that consists of a symmetric rigid body (gyro) that rotates about a fixed point similar to Lagrange’s gyroscope. This body is acted upon by external forces represented by a Newtonian force field, gyro torques about the principal axes of inertia of the gyro and perturbing moments acting on the same axes. Assuming that, the gyro initially has a high angular velocity about the dynamic axis of symmetry. The averaging technique is used to obtain a more appropriate averaging system for the governing system of equations of motion in terms of a smal

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28

Dhouib, S., R. Hbaieb, F. Chaari, M. S. Abbes, T. Fakhfakh, and M. Haddar. "Free vibration characteristics of compound planetary gear train sets." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 222, no. 8 (2008): 1389–401. http://dx.doi.org/10.1243/09544062jmes870.

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In this study, a plane model of a compound planetary gear train (CPGT) is proposed in order to study its free vibration characteristics. Two translations and one rotation are considered for each element (sun, carrier, ring-1, ring-2, and planets) of the CPGT. The contact between the teeth in mesh is modelled by linear springs with stiffness called gearmesh stiffness. The phasing between these stiffness is taken into account. Using Lagrange formulation, the equation of motion is derived. Starting from the eigenvalue problem of the system, the influence of the planets’ number and position, and t

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29

Kosov, Alexander A., and Eduard I. Semenov. "On exact solutions of equations of rotational motion of a rigid body under action of torque of circular-gyroscopic forces." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 23, no. 2 (2021): 159–70. http://dx.doi.org/10.15507/2079-6900.23.202102.159-170.

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Abstract. A nonlinear system of differential equations describing the rotational motion of a rigid body under the action of torque of potential and circular-gyroscopic forces is considered. For this torque, the system of differential equations has three classical first integrals: the energy integral, the area integral, and the geometric integral. For the analogue of the Lagrange case, when two moments of inertia coincide and the potential depends on one angle, an additional first integral is found and integration in quadratures is performed. A number of examples is considered where parametric

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Amer, T. S. "On the motion of a gyrostat similar to Lagrange’s gyroscope under the influence of a gyrostatic moment vector." Nonlinear Dynamics 54, no. 3 (2008): 249–62. http://dx.doi.org/10.1007/s11071-007-9327-x.

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31

Katz, Joseph, Shogo Inagaki, and Asher Yahalom. "Energy Principles for Self-Gravitating Barotropic Flows. I. General Theory." Publications of the Astronomical Society of Japan 45, no. 3 (1993): 421–30. https://doi.org/10.1093/pasj/45.3.421.

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Abstract The following principle of minimum energy may be a powerful substitute to the dynamical perturbation method when the latter is hard to apply. The fluid elements of self-gravitating barotropic flows, whose vortex lines extend to the boundary of the fluid, are labeled in such a way that any change in the trial configurations automatically preserves both the mass and circulation. The velocity field is given by a mass-conserving Clebsch representation. With three independent Lagrangian functions, the total energy is stationary for all small variations about a flow with fixed linear and an

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32

Chen, Chih-Keng, Trung-Dung Chu, and Xiao-Dong Zhang. "Modeling and Control of an Active Stabilizing Assistant System for a Bicycle." Sensors 19, no. 2 (2019): 248. http://dx.doi.org/10.3390/s19020248.

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This study designs and controls an active stabilizing assistant system (ASAS) for a bicycle. Using the gyroscopic effect of two spinning flywheels, the ASAS generates torques that assist the rider to stabilize the bicycle in various riding modes. Riding performance and the rider’s safety are improved. To simulate the system dynamic behavior, a model of a bicycle–rider system with the ASAS on the rear seat is developed. This model has 14 degrees of freedom and is derived using Lagrange equations. In order to evaluate the efficacy of the ASAS in interacting with the rider’s control actions, simu

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Zirkelback, Nicole L., and Jerry H. Ginsberg. "Ritz Series Analysis of Rotating Shaft System: Validation, Convergence, Mode Functions, and Unbalance Response." Journal of Vibration and Acoustics 124, no. 4 (2002): 492–501. http://dx.doi.org/10.1115/1.1501081.

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A shaft with attached rigid disks is modeled as a rotating Timoshenko beam supported by nonconservative, flexible 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 gyroscopic matr

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Gogoleva, N. F. "KINEMATICAL INTERPRETATION OF THE PARTIAL SOLUTION OF THE PROBLEM OF MOTION OF TWO LAGRANGE GYROSCOPES CONNECTED WITH A NON-HOLONOMIC HINGE." Naukovi praci Donec'kogo nacional'nogo tehnicnogo universitetu. Seria, Informatika, kibernetika i obcisluval'na tehnika 2, no. 25 (2017): 40–47. http://dx.doi.org/10.31474/1996-1588-2017-2-25-40-47.

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Gavrilyuk, Sergey. "‘Uncertainty’ principle in two fluid–mechanics." ESAIM: Proceedings and Surveys 69 (2020): 47–55. http://dx.doi.org/10.1051/proc/202069047.

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Hamilton’s principle (or principle of stationary action) is one of the basic modelling tools in finite-degree-of-freedom mechanics. It states that the reversible motion of mechanical systems is completely determined by the corresponding Lagrangian which is the difference between kinetic and potential energy of our system. The governing equations are the Euler-Lagrange equations for Hamil- ton’s action. Hamilton’s principle can be naturally extended to both one-velocity and multi-velocity continuum mechanics (infinite-degree-of-freedom systems). In particular, the motion of multi–velocity conti

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Tseng, Chaw-Wu, Jr-Yi Shen, Hyunchul Kim, and I. Y. Shen. "A Unified Approach to Analyze Vibration of Axisymmetric Rotating Structures with Flexible Stationary Parts." Journal of Vibration and Acoustics 127, no. 2 (2005): 125–38. http://dx.doi.org/10.1115/1.1857917.

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This paper demonstrates a unified approach to analyze linear vibration of rotating machines with arbitrary geometry and complexity. In this formulation, the rotating machine consists of three components: a rotating part (rotor), a stationary part (stator or housing), and multiple bearings. The rotor is assumed axisymmetric and spinning at constant speed. Moreover, the rotor and the housing have arbitrary geometry and complexity. The bearings connecting the rotor and housing could be rolling-element bearings or hydrodynamic bearings. The paper consists of three major sections: mathematical mode

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37

Kononov, Yuriy M. "On the rotational stability in an environment with resistance of a free system of two rigid bodies connected by an elastic spherical joint and having a cavity with a liquid." Ukrainian Mathematical Bulletin 21, no. 2 (2024): 205–19. https://doi.org/10.37069/1810-3200-2024-21-2-4.

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On the basis of the known equations of motion of the system of coupled gyrostats by P.V. Kharlamov and the functions of state by S.L. Sobolev, the equations of rotation in a medium with resistance of a free system of two elastically connected rigid bodies with cavities completely filled with an ideal incompressible fluid were derived. Rigid bodies are connected by an elastic restoring spherical joint. Assuming that the center of mass of the rigid bodies is located on the third main axis of inertia and the fluid is ideal, the equation of disturbed motion of the considered mechanical system is o

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38

Ren, Fei, Jinchen Ji, Guofu Luo, et al. "Investigation of Dynamic Load Sharing Behavior for Herringbone Planetary Gears considering Multicoupling Manufacturing Errors." Shock and Vibration 2021 (July 9, 2021): 1–15. http://dx.doi.org/10.1155/2021/5511817.

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In this study, based on the lumped-parameter theory and the Lagrange approach, a novel and generalized bending-torsional-axial coupled dynamic model for analyzing the load sharing behavior in the herringbone planetary gear train (HPGT) is presented by taking into account the actual structure of herringbone gears, manufacturing errors, time-dependent meshing stiffness, bearing deflections, and gyroscopic effects. The model can be applied to the analysis of the vibration of the HPGT with any number of planets and different types of manufacturing errors in different floating forms. The HPGT equiv

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Zhao, Tianyu, Yu Ma, Hongyuan Zhang, and Jie Yang. "Coupled Free Vibration of Spinning Functionally Graded Porous Double-Bladed Disk Systems Reinforced with Graphene Nanoplatelets." Materials 13, no. 24 (2020): 5610. http://dx.doi.org/10.3390/ma13245610.

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This paper presents, for the first time, the mechanical model and theoretical analysis of free vibration of a spinning functionally graded graphene nanoplatelets reinforced composite (FG-GPLRC) porous double-bladed disk system. The nanocomposite rotor is made of porous metal matrix and graphene nanoplatelet (GPL) reinforcement material with different porosity and nanofillers distributions. The effective material properties of the system are graded in a layer-wise manner along the thickness directions of the blade and disk. Considering the gyroscopic effect, the coupled model of the double-blad

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Castillo Pardo, Alejandro, Ioannis Goulos, and Vassilios Pachidis. "Modelling and analysis of coupled flap-lag-torsion vibration characteristics helicopter rotor blades." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 231, no. 10 (2016): 1804–23. http://dx.doi.org/10.1177/0954410016675891.

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This paper presents the development of a mathematical approach targeting the modelling and analysis of coupled flap-lag-torsion vibration characteristics of non-uniform continuous rotor blades. The proposed method is based on the deployment of Lagrange’s equation of motion to the three-dimensional kinematics of rotor blades. Modal properties derived from classical-beam and torsion theories are utilized as assumed deformation functions. The formulation, which is valid for hingeless, freely hinged and spring-hinged articulated rotor blades, is reduced to a set of closed-form integral expressions

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Shen, I. Y., and Hyunchul Kim. "A Linearized Theory on Ground-Based Vibration Response of Rotating Asymmetric Flexible Structures." Journal of Vibration and Acoustics 128, no. 3 (2006): 375–84. http://dx.doi.org/10.1115/1.2172265.

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This paper is to develop a unified algorithm to predict vibration of spinning asymmetric rotors with arbitrary geometry and complexity. Specifically, the algorithm is to predict vibration response of spinning rotors from a ground-based observer. 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

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Lv, Binglin, Wanyou Li, and Huajiang Ouyang. "Moving Force-Induced Vibration of a Rotating Beam with Elastic Boundary Conditions." International Journal of Structural Stability and Dynamics 15, no. 01 (2015): 1450035. http://dx.doi.org/10.1142/s0219455414500357.

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In this paper, an analytical technique, the so-called Fourier Spectral method (FSM), is extended to the vibration analysis of a rotating Rayleigh beam considering the gyroscopic effect. The model presented can have arbitrary boundary conditions specified in terms of elastic constraints in the translations and rotations or even in terms of attached lumped masses and inertias. Each displacement function is universally expressed as a linear combination of a standard Fourier cosine series and several supplementary functions introduced to ensure and accelerate the convergence of the series expansio

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Shen, I. Y. "Closed-Form Forced Response of a Damped, Rotating, Multiple Disks/Spindle System." Journal of Applied Mechanics 64, no. 2 (1997): 343–52. http://dx.doi.org/10.1115/1.2787313.

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This paper is to study forced vibration response of a rotating disk/spindle system consisting of multiple flexible circular disks clamped to a rigid spindle supported by two flexible bearings. In particular, the disk/spindle system is subjected to prescribed translational base excitations and externally applied loads. Because of the bearing flexibility, the rigid spindle undergoes infinitesimal rigid-body rocking and translation simultaneously. To model real vibration response that has finite resonance amplitudes, the disks and the bearings are assumed to be viscously damped. Equations of moti

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Khulief, Y. A., F. A. Al-Sulaiman, and S. Bashmal. "Vibration analysis of drillstrings with string—borehole interaction." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 222, no. 11 (2008): 2099–110. http://dx.doi.org/10.1243/09544062jmes968.

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Drillstring vibration is one of the major causes for a deteriorated drilling performance, and if left untreated may result in a complete failure of the drilling process. Although the variations in the drilling load, stick-slip, and whirling are known to be the primary causes of severe vibrations, they often give rise to excessive flexural deformations and subsequent string—borehole interaction. Drillstring contact-impact interaction with borehole results in high-frequency excitations, which further deteriorate the drilling performance, and may cause damage to the bottomhole assembly. Modelling

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Leshchenko, D., and T. Kozachenko. "SOME PROBLEMS ABOUT THE MOTION OF A RIGID BODY IN A RESISTIVE MEDIUM." Mechanics And Mathematical Methods 3, no. 2 (2021): 6–17. http://dx.doi.org/10.31650/2618-0650-2021-3-2-6-17.

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The dynamics of rotating rigid bodies is a classical topic of study in mechanics. In the eighteenth and nineteenth centuries, several aspects of a rotating rigid body motion were studied by famous mathematicians as Euler, Jacobi, Poinsot, Lagrange, and Kovalevskya. However, the study of the dynamics of rotating bodies of still important for aplications such as the dynamics of satellite-gyrostat, spacecraft, re-entry vehicles, theory of gyroscopes, modern technology, navigation, space engineering and many other areas. A number of studies are devoted to the dynamics of a rigid body in a resistiv

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K, Ramkumar. "Theory of Time – 2024 R (Universal Theory for Everything)." International Journal of Engineering & Science 13, no. 9 (2024): 29–296. http://dx.doi.org/10.9790/1813-130929296.

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“Theory of Time” is a research and analysis report on ‘All kind of Transformation processes’ to find out the reason for changes, this is a Universal Theory & applicable for all natural phenomena. I had found some systematic/ logical/ relational imbalance among the principles of AC Transformer, Ohm’s law, series parallel circuits and law of conservation of energy. I did systematic analysis and research on above said combination principles and identified / formulated/ organized a common transformation mechanism for all and is called ‘Universal Transformation System’(UTS). Here, relative comp

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Ismail, A. I. "Treating the Solid Pendulum Motion by the Large Parameter Procedure." International Journal of Aerospace Engineering 2020 (December 22, 2020): 1–8. http://dx.doi.org/10.1155/2020/8853867.

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In this paper, we consider the dynamical description of a pendulum model consists of a heavy solid connection to a nonelastic string which suspended on an elliptic path in a vertical plane. We suppose that the dimensions of the solid are large enough to the length of the suspended string, in contrast to previous works which considered that the dimensions of the body are sufficiently small to the length of the string. According to this new assumption, we define a large parameter ε and apply Lagrange’s equation to construct the equations of motion for this case in terms of this large parameter.

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Chen, Ying-Chung, Xu Feng Cheng, and Siu-Tong Choi. "Dynamic analysis of a helical geared rotor-bearing system with composite rotating shafts." Aircraft Engineering and Aerospace Technology 93, no. 10 (2021): 1699–708. http://dx.doi.org/10.1108/aeat-04-2021-0095.

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Purpose This study aims to study the dynamic characteristics of a helical geared rotor-bearing system with composite material rotating shafts. Design/methodology/approach A finite element model of a helical geared rotor-bearing system with composite material rotating shafts is developed, in which the rotating shafts of the system are composed of composite material and modeled as Timoshenko beam; a rigid mass is used to represent the gear and their gyroscopic effect is taken into account; bearings are modeled as linear spring-damper; and the equations of motion are obtained by applying Lagrange

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Kononov, Yu M., and Ya I. Svyatenko. "Stabilization of Unstable Spinning of a Lagrange Gyroscope in a Resisting Medium by Another Spinning Gyroscope." International Applied Mechanics, March 18, 2023. http://dx.doi.org/10.1007/s10778-023-01184-3.

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Aguessivognon, J. M., Clément Hodévèwan Miwadinou та A. V. Monwanou. "Eﬀect of biharmonic excitation on complex dynamics of a two-degree-of-freedom heavy symmetric gyroscope". Physica Scripta, 27 липня 2023. http://dx.doi.org/10.1088/1402-4896/aceb3d.

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Abstract This work analyzes the chaotic dynamics and the coexistence of attractors and their control in the complex dynamics of a rotating gyroscope modeled following Euler angles using the Lagrange approach. The fixed points of the system is checked and their stability analyzed. The complete dynamics of the gyroscope is studied and the coexistence of attractors analyzed using Runge-Kutta algorithm of order 4. It is obtained for appropriate conditions the coexistence of chaotic and/or regular attractors. The study also pointed out that the dissipation and the first integrals of the moments of

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