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Статті в журналах з теми "Symmetric rigid body"

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Автор: Grafiati

Опубліковано: 14 березня 2023

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1

Dragović, Vladimir, Borislav Gajić, and Božidar Jovanović. "Note on free symmetric rigid body motion." Regular and Chaotic Dynamics 20, no. 3 (May 2015): 293–308. http://dx.doi.org/10.1134/s1560354715030065.

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2

Celledoni, E., and N. Säfström. "A symmetric splitting method for rigid body dynamics." Modeling, Identification and Control: A Norwegian Research Bulletin 27, no. 2 (2006): 95–108. http://dx.doi.org/10.4173/mic.2006.2.2.

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3

Lian, Kuang-Yow, Li-Sheng Wang, and Li-Chen Fu. "A skew-symmetric property of rigid-body systems." Systems & Control Letters 33, no. 3 (March 1998): 187–97. http://dx.doi.org/10.1016/s0167-6911(97)00110-2.

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4

Amer, T. S. "The Rotational Motion of the Electromagnetic Symmetric Rigid Body." Applied Mathematics & Information Sciences 10, no. 4 (July 1, 2016): 1453–64. http://dx.doi.org/10.18576/amis/100424.

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5

Lv, Wen Jun, and Xin Sheng Ge. "Energy-Based Inverted Equilibrium of the Axially Symmetric 3D Pendulum." Applied Mechanics and Materials 138-139 (November 2011): 128–33. http://dx.doi.org/10.4028/www.scientific.net/amm.138-139.128.

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In this paper, we study the attitude control problems based on model of the 3D axially symmetric rigid pendulum. Three degrees of freedom pendulum (3D pendulum) is a rigid body supported by a frictionless pivot. According to relative position of the center of mass and the fixed pivot without friction, the 3D rigid pendulum can be divided into two balanced attitudes, Hanging equilibrium and inverted equilibrium. When the 3D rigid pendulum in axis symmetric case, the axis of symmetry is equivalent to axis of inertia of rigid body, and angular velocity around the axis of symmetry is constant that not equal to zero, as a result, the 3D rigid pendulum equal to the axisymmetric rigid pendulum. According to the motion attitude of the axially symmetric 3D pendulum, this article proposes a control method based on passivity, By analyzing the dynamic characteristics, and demonstrate the dynamic characteristics to meet the passive condition. Firstly, we use the passivity theory, from total energy of the system, to research the equilibrium stability of the axially symmetric 3D pendulum in the inverted position. Secondly, to utilize the passivity theory and the Lyapunov function that we proposed to deduce the control law based on the energy method, so that the axially symmetric 3D pendulum to reach asymptotically stable in equilibrium position, and the simulation results verify the availability of the method.

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6

Cohen, H., and G. P. Mac Sithigh. "Symmetric and asymmetric roto-deformations of a symmetrical, isotropic, elastic pseudo-rigid body." International Journal of Non-Linear Mechanics 27, no. 4 (July 1992): 519–26. http://dx.doi.org/10.1016/0020-7462(92)90058-f.

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7

Tsiotras, P., and J. M. Longuski. "Analytic Solutions for a Spinning Rigid Body Subject to Time-Varying Body-Fixed Torques, Part II: Time-Varying Axial Torque." Journal of Applied Mechanics 60, no. 4 (December 1, 1993): 976–81. http://dx.doi.org/10.1115/1.2901011.

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In this paper we extend the methodology developed in Part I in order to accommodate the case of an axial time-varying torque (in addition to the two transverse timevarying torques) acting on a rotating rigid body. The analytic solutions thus derived describe the general attitude motion of a near-symmetric rigid body subject to timevarying torques about all three body-fixed axes.

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8

Atchonouglo, K., and K. Nwuitcha. "MATRIX STUDY OF THE EQUATION OF SOLID RIGID MOTIONS." Advances in Mathematics: Scientific Journal 10, no. 9 (September 13, 2021): 3195–207. http://dx.doi.org/10.37418/amsj.10.9.9.

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In this article, we described the equations of motion of a rigid solid by a matrix formulation. The matrices contained in our movement description are homogeneous to the same unit. Inertial characteristics are met in a 4x4 positive definite symmetric matrix called "tensor generalized Poinsot." This matrix consists of 3x3 positive definite symmetric matrix called "inertia tensor Poinsot", the coordinates of the center of mass multiplied by the total body mass and the total mass of the rigid body. The equations of motion are formulated as a gender skew 4x4 matrices. They summarize the "principle of fundamental dynamics". The Poinsot generalized tensor appears linearly in this equality as required by the linear dependence of the equations of motion with the ten characteristics inertia of the rigid solid.

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9

Maciejewski, Andrzej J. "Chaos and order in the Rotational Motion." International Astronomical Union Colloquium 132 (1993): 23–38. http://dx.doi.org/10.1017/s0252921100065891.

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AbstractIt was proved that the problem of perturbed planar oscillations of a rigid-body in a circular orbit is nonitegrable. Two types of perturbations were considered: solar radiations pressure and the third body torques. In the second part of the paper example of chaotic rotations of a symmetric rigid body in a circular orbit was given. It was shown numerically that the phase space is divided into two separate regions of chaotic and ordered motions.

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10

Bloch, Anthony M., Peter E. Crouch, Jerrold E. Marsden, and Tudor S. Ratiu. "The symmetric representation of the rigid body equations and their discretization." Nonlinearity 15, no. 4 (June 17, 2002): 1309–41. http://dx.doi.org/10.1088/0951-7715/15/4/316.

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11

Shamolin, M. V. "CASES OF INTEGRABILITY CORRESPONDING TO THE PENDULUM MOTION IN FOUR-DIMENSIONAL SPACE." Vestnik of Samara University. Natural Science Series 23, no. 1 (September 20, 2017): 41–58. http://dx.doi.org/10.18287/2541-7525-2017-23-1-41-58.

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Анотація:

In this article, we systemize some results on the study of the equations of motion of dynamically symmetric fixed four-dimensional rigid bodies–pendulums located in a nonconservative force fields. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of a medium. In parallel, we study the problem of the motion of a free four-dimensional rigid body also located in a similar force fields. Herewith, this free rigid body is influenced by a nonconservative tracing force; under action of this force, either the magnitude of the velocity of some characteristic point of the body remains constant, which means that the system possesses a nonintegrable servo constraint. We also show the nontrivial topological and mechanical analogies.

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12

Vulovic, Ivan, Qing Yao, Young-Jun Park, Alexis Courbet, Andrew Norris, Florian Busch, Aniruddha Sahasrabuddhe, et al. "Generation of ordered protein assemblies using rigid three-body fusion." Proceedings of the National Academy of Sciences 118, no. 23 (June 1, 2021): e2015037118. http://dx.doi.org/10.1073/pnas.2015037118.

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Protein nanomaterial design is an emerging discipline with applications in medicine and beyond. A long-standing design approach uses genetic fusion to join protein homo-oligomer subunits via α-helical linkers to form more complex symmetric assemblies, but this method is hampered by linker flexibility and a dearth of geometric solutions. Here, we describe a general computational method for rigidly fusing homo-oligomer and spacer building blocks to generate user-defined architectures that generates far more geometric solutions than previous approaches. The fusion junctions are then optimized using Rosetta to minimize flexibility. We apply this method to design and test 92 dihedral symmetric protein assemblies using a set of designed homodimers and repeat protein building blocks. Experimental validation by native mass spectrometry, small-angle X-ray scattering, and negative-stain single-particle electron microscopy confirms the assembly states for 11 designs. Most of these assemblies are constructed from designed ankyrin repeat proteins (DARPins), held in place on one end by α-helical fusion and on the other by a designed homodimer interface, and we explored their use for cryogenic electron microscopy (cryo-EM) structure determination by incorporating DARPin variants selected to bind targets of interest. Although the target resolution was limited by preferred orientation effects and small scaffold size, we found that the dual anchoring strategy reduced the flexibility of the target-DARPIN complex with respect to the overall assembly, suggesting that multipoint anchoring of binding domains could contribute to cryo-EM structure determination of small proteins.

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13

Kononov, Yu, O. Dovgoshey, and A. K. Cheib. "ON THE STABILITY OF UNIFORM ROTATION IN A RESISTING NONSYMETRIC RIGID BODY UNDER THE ACTION OF A CONSTANT MOMENT IN INERTIAL REFERENCE FRAME." Mechanics And Mathematical Methods 4, no. 1 (June 2022): 6–22. http://dx.doi.org/10.31650/2618-0650-2022-4-1-6-22.

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Assuming that the center of mass of a rigid asymmetric body is on the third main axis of inertia of a rigid body, the conditions for the asymptotic stability of uniform rotation of a dynamically asymmetric solid rigid body with a fixed point are obtained. These conditions are obtained in the form of a system of three inequalities based on the Lénard-Shipar test, written in innormal form. The rigid body is under the action of gravity, dissipative moment and constant moment in the inertial frame of reference. The rotation of a rigid asymmetric body around the center of mass is studied. Uniform rotation around the center of mass of a rigid asymmetric body will be unstable in the absence of a constant moment. Cases of absence of dynamic or dissipative asymmetry are considered. It is shown that the equilibrium position of a rigid body will be stable only under the action of the reducing moment. Dynamic asymmetry has a more significant effect on the stability of rotation of an asymmetric rigid body than dissipative asymmetry. Stability conditions have been studied for various limiting cases of small or large values of restoring, overturning, or constant moments. It is noted that for sufficiently large values of the modulus of the reducing moment, the rotation of the asymmetric solid will be asymptomatically stable. If the axial moment of inertia is the greatest or the smallest moment of inertia, then at sufficiently large values of angular velocity, both under the action of the overturning moment and under the action of the reducing moment, the rotation of the asymmetric solid will be asymptomatically stable. Analytical studies of the influence of dissipative, constant, overturning and restorative moments on the stability of uniform rotations of asymmetric and symmetric solids have been carried out. It is shown that in the absence of dynamic and dissipative symmetries, the obtained stability conditions coincide with the known ones.

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14

Shamolin, Maxim V. "Cases of Integrability Which Correspond to the Motion of a Pendulum in the Three-dimensional Space." WSEAS TRANSACTIONS ON APPLIED AND THEORETICAL MECHANICS 16 (August 10, 2021): 73–84. http://dx.doi.org/10.37394/232011.2021.16.8.

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We systematize some results on the study of the equations of spatial motion of dynamically symmetric fixed rigid bodies–pendulums located in a nonconservative force fields. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of a medium. In parallel, we study the problem of a spatial motion of a free rigid body also located in a similar force fields. Herewith, this free rigid body is influenced by a nonconservative tracing force; under action of this force, either the magnitude of the velocity of some characteristic point of the body remains constant, which means that the system possesses a nonintegrable servo constraint, or the center of mass of the body moves rectilinearly and uniformly; this means that there exists a nonconservative couple of forces in the system

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15

Ohsawa, Tomoki. "The symmetric representation of the generalized rigid body equations and symplectic reduction." Journal of Physics A: Mathematical and Theoretical 52, no. 36 (August 13, 2019): 36LT01. http://dx.doi.org/10.1088/1751-8121/ab20db.

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16

Amer, T. S., and W. S. Amer. "The Rotational Motion of a Symmetric Rigid Body Similar to Kovalevskaya’s Case." Iranian Journal of Science and Technology, Transactions A: Science 42, no. 3 (March 27, 2017): 1427–38. http://dx.doi.org/10.1007/s40995-017-0221-1.

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17

Andriano, Valeria. "Global feedback stabilization of the angular velocity of a symmetric rigid body." Systems & Control Letters 20, no. 5 (May 1993): 361–64. http://dx.doi.org/10.1016/0167-6911(93)90014-w.

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18

Shamolin, M. V. "CASES OF INTEGRABILITY CORRESPONDING TO THE PENDULUM MOTION IN THREE-DIMENSIONAL SPACE." Vestnik of Samara University. Natural Science Series 22, no. 3-4 (April 14, 2017): 75–97. http://dx.doi.org/10.18287/2541-7525-2016-22-3-4-75-97.

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Анотація:

In this article, we systemize some results on the study of the equations of spatial motion of dynamically symmetric fixed rigid bodies–pendulums located in a nonconservative force fields. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of a medium. In parallel, we study the problem of a spatial motion of a free rigid body also located in a similar force fields. Herewith, this free rigid body is influenced by a nonconservative tracing force; under action of this force, either the magnitude of the velocity of some characteristic point of the body remains constant, which means that the system possesses a nonintegrable servo constraint. The obtained results are systematized and served in the invariant form. We also show the nontrivial topological and mechanical analogies.

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19

Zub, Stanislav S. "Hamiltonian Dynamics of the Symmetric Top in External Axially-Symmetric Fields. Magnetic Retention of a Rigid Body." Journal of Automation and Information Sciences 50, no. 7 (2018): 48–69. http://dx.doi.org/10.1615/jautomatinfscien.v50.i7.50.

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20

Karapetyan, Alexander, and Alexander Kuleshov. "The Routh theorem for mechanical systems with unknown first integrals." Theoretical and Applied Mechanics 44, no. 2 (2017): 169–80. http://dx.doi.org/10.2298/tam170512008k.

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In this paper we discuss problems of stability of stationary motions of conservative and dissipative mechanical systems with first integrals. General results are illustrated by the problem of motion of a rotationally symmetric rigid body on a perfectly rough plane.

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21

Starek, L., D. J. Inman, and A. Kress. "A Symmetric Inverse Vibration Problem." Journal of Vibration and Acoustics 114, no. 4 (October 1, 1992): 564–68. http://dx.doi.org/10.1115/1.2930299.

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This paper considers the inverse eigenvalue problem for linear vibrating systems described by a vector differential equation with constant coefficient matrices. The inverse problem of interest here is that of determining real symmetric coefficient matrices, assumed to represent the mass, damping, and stiffness matrices, given the natural frequencies and damping ratios of the structure (i.e., the system eigenvalues). The approach presented here allows for repeated eigenvalues, whether simple or not, and for rigid body modes. The method is algorithmic and results in a computer code for determining mass normalized damping, and stiffness matrices for the case that each mode of the system is underdamped.

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22

Goździewski, K., and A.J. Maciejewski. "Perturbations of Small Moons Orbits due to their rotation: The Model Problem." International Astronomical Union Colloquium 172 (1999): 379–80. http://dx.doi.org/10.1017/s0252921100072808.

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We consider here the spin—orbit coupling influence on the relative orbital motion of two bodies interacting gravitationally. We assume that one of the bodies is spherically symmetric and the other possesses a plane of dynamical symmetry. In the full non-linear settings, this problem permits coplanar motion when the mass center of the spherically symmetric body moves in the plane. We used this simple model for a qualitative estimation of the changes of the relative orbit in two cases: A) the Sun-asteroid case (the fast rotating rigid body), B) a small satellite of a big planet in resonant rotation.The motion is described in the rigid body fixed frame. An appropriate change of physical units (Goźdiewski,1998a) leads to nondimensional dynamical variables and parameters. After that the Hamiltonian of the problem, written in polar variables, is the followingwhere (I1, I2, I3) are the principal moments of inertia, (r, φ) are the relative polar coordinates of the point mass in the body frame, (Pr, pφ) are the canonical momenta, (G3 represents the constant of total angular momentum, ε = (ro/r)2, and ro is the mean radius of the body.

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23

SHAMOLIN, MAXIM V. "VARIETY OF THE CASES OF INTEGRABILITY IN DYNAMICS OF A SYMMETRIC 2D-, 3D- AND 4D-RIGID BODY IN A NONCONSERVATIVE FIELD." International Journal of Structural Stability and Dynamics 13, no. 07 (August 23, 2013): 1340011. http://dx.doi.org/10.1142/s0219455413400117.

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A vast number of papers are devoted to studying the complete integrability of equations of four-dimensional rigid-body motion. Although in studying low-dimensional equations of motion of quite concrete (two- and three-dimensional) rigid bodies in a nonconservative force field, the author arrived at the idea of generalizing the equations to the case of a four-dimensional rigid body in an analogous nonconservative force field. As a result of such a generalization, the author obtained the variety of cases of integrability in the problem of body motion in a resisting medium that fills the four-dimensional space in the presence of a certain tracing force that allows one to reduce the order of the general system of dynamical equations of motion in a methodical way.

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24

Vereshchagin, Mikhail, Andrzej J. Maciejewski, and Krzysztof Goździewski. "Relative equilibria in the unrestricted problem of a sphere and symmetric rigid body." Monthly Notices of the Royal Astronomical Society 403, no. 2 (February 4, 2010): 848–58. http://dx.doi.org/10.1111/j.1365-2966.2009.16158.x.

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25

Burov, A. A., and V. I. Nikonov. "On the Approximation of a Nearly Dynamically Symmetric Rigid Body by Two Balls." Computational Mathematics and Mathematical Physics 62, no. 12 (December 2022): 2154–60. http://dx.doi.org/10.1134/s0965542522120053.

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26

Zˇefran, Milosˇ, and Vijay Kumar. "A Geometrical Approach to the Study of the Cartesian Stiffness Matrix." Journal of Mechanical Design 124, no. 1 (October 1, 1998): 30–38. http://dx.doi.org/10.1115/1.1423638.

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The stiffness of a rigid body subject to conservative forces and moments is described by a tensor, whose components are best described by a 6×6 Cartesian stiffness matrix. We derive an expression that is independent of the parameterization of the motion of the rigid body using methods of differential geometry. The components of the tensor with respect to a basis of twists are given by evaluating the tensor on a pair of basis twists. We show that this tensor depends on the choice of an affine connection on the Lie group, SE3. In addition, we show that the definition of the Cartesian stiffness matrix used in the literature [1,2] implicitly assumes an asymmetric connection and this results in an asymmetric stiffness matrix in a general loaded configuration. We prove that by choosing a symmetric connection we always obtain a symmetric Cartesian stiffness matrix. Finally, we derive stiffness matrices for different connections and illustrate the calculations using numerical examples.

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27

Bardin, B. S., E. A. Chekina, and A. M. Chekin. "On the Orbital Stability of Pendulum Oscillations of a Dynamically Symmetric Satellite." Nelineinaya Dinamika 18, no. 4 (2022): 0. http://dx.doi.org/10.20537/nd221211.

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The orbital stability of planar pendulum-like oscillations of a satellite about its center of mass is investigated. The satellite is supposed to be a dynamically symmetrical rigid body whose center of mass moves in a circular orbit. Using the recently developed approach [1], local variables are introduced and equations of perturbed motion are obtained in a Hamiltonian form. On the basis of the method of normal forms and KAM theory, a nonlinear analysis is performed and rigorous conclusions on orbital stability are obtained for almost all parameter values. In particular, the so-called case of degeneracy, when it is necessary to take into account terms of order six in the expansion of the Hamiltonian function, is studied.

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28

Markeev, A. P. "On the motion of a heavy dynamically symmetric rigid body with vibrating suspension point." Mechanics of Solids 47, no. 4 (July 2012): 373–79. http://dx.doi.org/10.3103/s0025654412040012.

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29

Smirnov, Georgi V. "Attitude determination and stabilization of a spherically symmetric rigid body in a magnetic field." International Journal of Control 74, no. 4 (January 2001): 341–47. http://dx.doi.org/10.1080/00207170010010560.

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30

HEDREA, CIPRIAN, ROMEO NEGREA, and IOAN ZAHARIE. "THE 1/2 CORRECTION FORMS IN GEOMETRIC QUANTIZATION OF THE SYMMETRIC FREE RIGID BODY." International Journal of Geometric Methods in Modern Physics 09, no. 07 (September 7, 2012): 1220011. http://dx.doi.org/10.1142/s0219887812200113.

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31

Kononov, Yu, та A. K. Cheib. "ІNFLUENCE OF DYNAMIC ASYMMETRY ON THE ROTATION STABILITY IN A RESISTING MEDIUM OF A ASYMMETRIC RIGID BODY UNDER THE ACTION OF A CONSTANT MOMENT IN INERTIAL REFERENCE FRAME". Mechanics And Mathematical Methods 4, № 2 (31 грудня 2022): 6–18. http://dx.doi.org/10.31650/2618-0650-2022-4-2-6-18.

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Анотація:

Under the assumption that the center of mass of an asymmetric rigid body is located on the third principal axis of inertia of a rigid body, the previously obtained conditions for the asymptotic stability of uniform rotation in a medium with resistance of a dynamically asymmetric rigid body are investigated. A rigid body rotates around a fixed point, is under the action of gravity, dissipative moment and constant moment in an inertial frame of reference. The stability conditions are presented as a system of three inequalities. The first and second inequalities have the first degree relative to the dynamic unbalance, and the third inequality has the third degree. The first and third inequalities are of the second degree with respect to the overturning or restoring moment, and the second inequality is of the first degree. The first and third inequalities are of the fourth degree with respect to the constant moment, and the second inequality is of the second degree. The third inequality is the most difficult to study. Analytical studies of the influence of dynamic unbalance, restoring and overturning moments on the conditions of asymptotic stability are carried out. Conditions for the asymptotic stability of uniform rotation in a medium with resistance to an asymmetric rigid body are obtained for sufficiently small values of dynamic unbalance. Sufficient stability conditions are written out up to the second order of smallness with respect to the constant moment and the first order of smallness with respect to the restoring and overturning moments. Instability conditions are obtained for sufficiently large dynamic unbalance. The effect of dynamic unbalance on the stability conditions for the rotation of a rigid body around the center of mass is studied. It is shown that in the absence of dissipative asymmetry, it is sufficient for asymptotic stability that the axial moment of inertia of a rigid body be greater than the double equatorial moment and that the well-known necessary stability condition for a symmetric rigid body be satisfied.

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32

Tkhai, Valentin N. "Equilibria and oscillations in a reversible mechanical system." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 8, no. 4 (2021): 709–15. http://dx.doi.org/10.21638/spbu01.2021.416.

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Анотація:

The paper investigates symmetric periodic motions (SPM) of reversible mechanical systems. A solution is given to the problem of bilateral continuation of a nondegenerate SPM to the global family of such SPMs. The result is applied to the general case of Euler’s problem on a heavy rigid body, when the body parameters are not bound by equality conditions and two families of pendulum oscillations are found connecting the lower and upper equilibria.

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33

Tsiotras, P., and J. M. Longuski. "A complex analytic solution for the attitude motion of a near-symmetric rigid body under body-fixed torques." CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY 51, no. 3 (1991): 281–301. http://dx.doi.org/10.1007/bf00051695.

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34

Schastok, J., M. Soffel, H. Ruder, and M. Schneider. "The post - Newtonian rotation of Earth: a first approach." Symposium - International Astronomical Union 128 (1988): 341–47. http://dx.doi.org/10.1017/s0074180900119709.

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Анотація:

The problems of dynamics of extended bodies in metric theories of gravity are reviewed. In a first approach towards the relativistic description of the Earth's rotational motion the post - Newtonian treatment of the free precession of a pseudo - rigid and axially symmetric model Earth is presented. Definitions of angular momentum, pseudo - rigidity, the corotating frame, tensor of inertia and axial symmetry of the rotating body are based upon the choice of the standard post - Newtonian (PN) coordinates and the full PN energy momentum complex. In this framework, the relation between angular momentum and angular (coordinate) velocity is obtained. Since the PN Euler equations for the angular velocity here formally take their usual Newtonian form it is concluded that apart from PN modifications (renormalizations) of the inertia tensor, the rotational motion of our pseudo - rigid and axially symmetric model Earth essentially is “Newtonian”.

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35

Longuski, J. M., and P. Tsiotras. "Analytical Solutions for a Spinning Rigid Body Subject to Time-Varying Body-Fixed Torques, Part I: Constant Axial Torque." Journal of Applied Mechanics 60, no. 4 (December 1, 1993): 970–75. http://dx.doi.org/10.1115/1.2901010.

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Анотація:

Analytic solutions are derived for the general attitude motion of a near-symmetric rigid body subject to time-varying torques in terms of certain integrals. A methodology is presented for evaluating these integrals in closed form. We consider the case of constant torque about the spin axis and of transverse torques expressed in terms of polynomial functions of time. For an axisymmetric body with constant axial torque, the resulting solutions of Euler’s equations of motion are exact. The analytic solutions for the Eulerian angles are approximate owing to a small angle assumption, but these apply to a wide variety of practical problems. The case when all three components of the external torque vector vary simultaneously with time is much more difficult and is treated in Part II.

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Panciroli, Riccardo, and Giangiacomo Minak. "Cavity Formation during Asymmetric Water Entry of Rigid Bodies." Applied Sciences 11, no. 5 (February 25, 2021): 2029. http://dx.doi.org/10.3390/app11052029.

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This work numerically evaluates the role of advancing velocity on the water entry of rigid wedges, highlighting its influence on the development of underpressure at the fluid–structure interface, which can eventually lead to fluid detachment or cavity formation, depending on the geometry. A coupled FEM–SPH numerical model is implemented within LS-DYNA, and three types of asymmetric impacts are treated: (I) symmetric wedges with horizontal velocity component, (II) asymmetric wedges with a pure vertical velocity component, and (III) asymmetric wedges with a horizontal velocity component. Particular attention is given to the evolution of the pressure at the fluid–structure interface and the onset of fluid detachment at the wedge tip and their effect on the rigid body dynamics. Results concerning the tilting moment generated during the water entry are presented, varying entry depth, asymmetry, and entry velocity. The presented results are important for the evaluation of the stability of the body during asymmetric slamming events.

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37

KAMBAYASHI, Atsushi, Harutoshi KOBAYASHI, and Keiichiro SONODA. "Applicability of a Rigid Body Spring Model to Impact Problems of Axi-symmetric Elastic Bodies." Journal of applied mechanics 2 (1999): 271–78. http://dx.doi.org/10.2208/journalam.2.271.

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38

Hedrea, Ciprian, Romeo Negrea, and Ioan Zaharie. "Retraction: The 1/2 correction forms in geometric quantization of the symmetric free rigid body." International Journal of Geometric Methods in Modern Physics 16, no. 06 (June 2019): 1993001. http://dx.doi.org/10.1142/s0219887819930010.

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The Romanian National Committee of Ethics has detected plagiarism in this article. Its publication status is now retracted with immediate effect from IJGMMP. Publisher's Note: As of 8th June 2020, the case is under dispute and pending for final court decision. http://portal.just.ro/30/SitePages/Dosar.aspx?id_dosar=3000000000111746&id_inst=30 https://curteadeapeltimisoara.eu/Detalii_Dosar.aspx?id=9556%2f30%2f2015&idinstanta=59

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MORITA, Yoshifumi, Fumitoshi MATSUNO, Motohisa IKEDA, Yukihiro KOBAYASHI, Hiroyuki UKAI, and Hisashi KANDO. "PDS Control of a One-Link Flexible Arm with a Non-Symmetric Rigid Tip Body." Transactions of the Institute of Systems, Control and Information Engineers 16, no. 1 (2003): 29–37. http://dx.doi.org/10.5687/iscie.16.29.

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40

Davidson, W. "A Petrov type I cylindrically symmetric solution for perfect fluid in steady rigid body rotation." Classical and Quantum Gravity 13, no. 2 (February 1, 1996): 283–87. http://dx.doi.org/10.1088/0264-9381/13/2/016.

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41

Mavraganis, A. G. "On the existence of symmetric periodic motions of a rigid body about a fixed point." Mechanics Research Communications 17, no. 3 (May 1990): 129–34. http://dx.doi.org/10.1016/0093-6413(90)90039-f.

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42

PIIROINEN, PETRI T., HARRY J. DANKOWICZ, and ARNE B. NORDMARK. "ON A NORMAL-FORM ANALYSIS FOR A CLASS OF PASSIVE BIPEDAL WALKERS." International Journal of Bifurcation and Chaos 11, no. 09 (September 2001): 2411–25. http://dx.doi.org/10.1142/s0218127401003462.

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This paper implements a center-manifold technique to arrive at a normal-form for the natural dynamics of a passive, bipedal rigid-body mechanism in the vicinity of infinite foot width and near-symmetric body geometry. In particular, numerical schemes are developed for finding approximate forms of the relevant invariant manifolds and the near-singular dynamics on these manifolds. The normal-form approximations are found to be highly accurate for relatively large foot widths with a range of validity extending to widths on the order of the mechanisms' height.

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43

Klekovkin, A. V., Yu L. Karavaev, and I. S. Mamaev. "The Control of an Aquatic Robot by a Periodic Rotation of the Internal Flywheel." Nelineinaya Dinamika 19, no. 1 (2023): 0. http://dx.doi.org/10.20537/nd230301.

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This paper presents the design of an aquatic robot actuated by one internal rotor. The robot body has a cylindrical form with a base in the form of a symmetric airfoil with a sharp edge. For this object, equations of motion are presented in the form of Kirchhoff equations for rigid body motion in an ideal fluid, which are supplemented with viscous resistance terms. A prototype of the aquatic robot with an internal rotor is developed. Using this prototype, experimental investigations of motion in a fluid are carried out.

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44

Grobbelaar-Van Dalsen, Maríe, and Niko Sauer. "Dynamic boundary conditions for the Navier–Stokes equations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 113, no. 1-2 (1989): 1–11. http://dx.doi.org/10.1017/s030821050002391x.

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SynopsisWhen a symmetric rigid body performs a rotation in a fluid, the system of governing equations consists of conservation of linear momentum of the fluid and conservation of angular momentum of the rigid body. Since the torque at the interface involves the drag due to the fluid flow, the conservation of angular momentum may be viewed as a boundary condition for the field equations of fluid motion. These equations at the boundary contain a time derivative and thus are of a dynamic nature. The familiar no-slip condition becomes an additional equation in the system which not only governs the fluid motion, but also the motion of the rigid body. The unknown functions in the system of equations are the velocity and pressure fields of the fluid motion and the angular velocity of the rigid body.In this paper we formulate the physical problem for the case of rotation about an axis of symmetry as an abstract ordinary differential equation in two Banach spaces in which the velocity field is the only unknown. To achieve this, a method for the elimination of the pressure field, which also occurs in the boundary condition, is developed. Existence and uniqueness results for the abstract equation are derived with the aid of the theory of B-evolutions and the associated theory of fractional powers of a closed pair of operators.

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45

Tawfik, Tawfik El-Sayed. "Attitude Control of an Axi-Symmetric Rigid Body Using Two Controls without Angular Velocity Measurements Paper." World Journal of Mechanics 03, no. 05 (2013): 1–5. http://dx.doi.org/10.4236/wjm.2013.35a001.

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46

Zinkevich, Ya S. "Quasi-optimal deceleration of rotational motion of a dynamically symmetric rigid body in a resisting medium." Mechanics of Solids 51, no. 2 (March 2016): 156–60. http://dx.doi.org/10.3103/s0025654416020035.

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47

Shamolin, M. V. "Classification of complete integrability cases in four-dimensional symmetric rigid-body dynamics in a nonconservative field." Journal of Mathematical Sciences 165, no. 6 (March 2010): 743–54. http://dx.doi.org/10.1007/s10958-010-9838-8.

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Ko, Y. Y. "Removing Non-Uniqueness in Symmetric Galerkin Boundary Element Method for Elastostatic Neumann Problems and its Application to Half-Space Problems." Journal of Mechanics 36, no. 6 (May 7, 2020): 749–61. http://dx.doi.org/10.1017/jmech.2020.15.

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ABSTRACTWhen the Symmetric Galerkin boundary element method (SGBEM) based on full-space elastostatic fundamental solutions is used to solve Neumann problems, the displacement solution cannot be uniquely determined because of the inevitable rigid-body-motion terms involved. Several methods that have been used to remove the non-uniqueness, including additional point support, eigen decomposition, regularization of a singular system and modified boundary integral equations, were introduced to amend SGBEM, and were verified to eliminate the rigid body motions in the solutions of full-space exterior Neumann problems. Because half-space problems are common in geotechnical engineering practice and they are usually Neumann problems, typical half-space problems were also analyzed using the amended SGBEM with a truncated free surface mesh. However, various levels of errors showed for all the methods of removing non-uniqueness investigated. Among them, the modified boundary integral equations based on the Fredholm’s theory is relatively preferable for its accurate results inside and near the loaded area, especially where the deformation varies significantly.

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Sapunkov, Ya G., A. V. Molodenkov, and T. V. Molodenkova. "Algorithm of the Time-Optimal Reorientation of an Axially Symmetric Spacecraft in the Class of Conical Motions." Mekhatronika, Avtomatizatsiya, Upravlenie 19, no. 12 (December 8, 2018): 10–17587. http://dx.doi.org/10.17587/mau.19.797-805.

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The problem of the time-optimal turn of a spacecraft as a rigid body with one axis of symmetry and bounded control function in absolute value is considered in the quaternion statement. For simplifying problem (concerning dynamic Euler equations), we change the variables reducing the original optimal turn problem of axially symmetric spacecraft to the problem of optimal turn of the rigid body with spherical mass distribution including one new scalar equation. Using the Pontryagin maximum principle, a new analytical solution of this problem in the class of conical motions is obtained. Algorithm of the optimal turn of a spacecraft is given. An explicit expression for the constant in magnitude optimal angular velocity vector of a spacecraft is found. The motion trajectory of a spacecraft is a regular precession. The conditions for the initial and terminal values of a spacecraft angular velocity vector are formulated. These conditions make it possible to solve the problem analytically in the class of conical motions. The initial and the terminal vectors of spacecraft angular velocity must be on the conical surface generated by arbitrary given constant conditions of the problem. The numerical example is presented. The example contain optimal reorientation of the Space Shuttle in the class of conical motions.

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Vishenkova, E. A., and O. V. Kholostova. "A study of permanent rotations of a heavy dynamically symmetric rigid body with a vibrating suspension point." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 27, no. 4 (December 2017): 590–607. http://dx.doi.org/10.20537/vm170409.

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