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The equations of motion of a rigid body acted upon by general conservative potential and gyroscopic forces were reduced by Yehia to a single second-order differential equation. The reduced equation was used successfully in the study of stability of certain simple motions of the body. In the present work we use the reduced equation to construct a new particular solution of the dynamics of a rigid body about a fixed point in the approximate field of a far Newtonian centre of attraction. Using a transformation to a rotating frame we also construct a new solution of the problem of motion of a multiconnected rigid body in an ideal incompressible fluid. It turns out that the solutions obtained generalize a known solution of the simplest problem of motion of a heavy rigid body about a fixed point due to Dokshevich. 相似文献
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A. A. Kireenkov 《Mechanics of Solids》2010,45(2):166-175
We suggest an exact integral model of sliding and spinning friction constructed under the assumption that the Coulomb law
in generalized differential form holds for the surface element in the interior of the contact spot. 相似文献
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Nikola Popović Dirk Praetorius Anja Schlömerkemper 《Continuum Mechanics and Thermodynamics》2007,19(1-2):67-80
The mathematical and physical analysis of magnetoelastic phenomena is a topic of ongoing research. Different formulae have
been proposed to describe the magnetic forces in macroscopic systems. We discuss several of these formulae in the context
of rigid magnetized bodies. In case the bodies are in contact, we consider formulae both in the framework of macroscopic electrodynamics
and via a multiscale approach, i.e., in a discrete setting of magnetic dipole moments. We give mathematically rigorous proofs
for domains of polygonal shape (as well as for more general geometries) in two and three space dimensions. In an accompanying
second article, we investigate the formulae in a number of numerical experiments, where we focus on the dependence of the
magnetic force on the distance between the bodies and on the case when the two bodies are in contact. The aim of the analysis
as well as of the numerical simulation is to contribute to the ongoing debate about which formula describes the magnetic force
between macroscopic bodies best and to stimulate corresponding real-life experiments.
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H.M. Yehia 《Mechanics Research Communications》1997,24(3):663
Some qualitative aspects of the problem of motion about a fixed point of a rigid body with a particle moving in it in a prescibed (sinusoidal) way was treated in [1–3]. The mechanical system comprised of a rigid body containing an internal mass that moves along a fixed line in the body was considered in several works [4–5]. Recently, an integrable case of this system was found, in which the body is dynamically axisymmetric and moves under no external forces while the particle moves on the axis of dynamical symmetry under the action of Hooke's force to the fixed point [5].In the present note we introduce a more general integrable case in which the particle moves on the axis of dynamical symmetry and is subject to an arbitary conservative force that depends only on the distance from the fixed point. Separation of variables is accomplished and the solution is reduced to quadratures. As a special version of this problem, the case when the particle bounces elastically between two points is briefly discussed. 相似文献
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Nonlinear Dynamics - This study aims to extend the application of the bi-potential method to solve the dynamics problems of rigid bodies involving friction and multiple impacts. The key issue is... 相似文献
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S. P. Timoshenko Institute of Mechanics, Ukrainian Academy of Sciences, Kiev. Lvov University. Translated from Prikladnaya Mekhanika, Vol. 30, No. 5, pp. 19–23, May, 1994. 相似文献
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A symmetric mathematical model is developed to describe the spatial motion of a system of space vehicles whose structure is
represented by regular geometrical figures (Platonic bodies). The model is symmetrized by using the Euler-Lagrange equations
of motion, the Rodrigues-Hamilton parameters, and quaternion matrix mathematics. The results obtained enable us to model a
wide range of dynamic, control, stabilization, and orientation problems for complex systems and to solve various problems
of dynamic design for such systems, including estimation of dynamic loading on the basic structure during maneuvers in space
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 126–132, January 2006. 相似文献
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A nonlinear mathematical model of a system of n rigid bodies undergoing translational vibrations under inertial loading is
constructed. The system includes ball supports as a seismic-isolation mechanism and electromagnetic dampers controlled via
an inertial feedback channel. A system of differential dynamic equations in normal form describing accelerative damping is
derived. The frequencies of small undamped vibrations are calculated. A method for analyzing the dynamic coefficients of rigid
bodies subject to accelerative damping is developed. The double phase–frequency resonance of a two-mass system is studied 相似文献
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Y. -G. Oh N. Sreenath P. S. Krishnaprasad J. E. Marsden 《Journal of Dynamics and Differential Equations》1989,1(3):269-298
We give a complete bifurcation and stability analysis for the relative equilibria of the dynamics of three coupled planar rigid bodies. We also use the equivariant Weinstein-Moser theorem to show the existence of two periodic orbits distinguished by symmetry type near the stable equilibrium. Finally we prove that the dynamics is chaotic in the sense of Poincaré-Birkhoff-Smale horseshoes using the version of Melnikov's method suitable for systems with symmetry due to Holmes and Marsden. 相似文献
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B.D. Reddy 《Journal of the mechanics and physics of solids》1981,29(3):199-210
A pair of dual extremum principles is derived for a rigid perfectly-plastic body subjected to dynamic loading. No restrictions are placed on the magnitude of the deformation. A Lagrangian formulation is used, and the dual principles are obtained in a systematic manner by using a saddle-shaped functional and a pair of operators adjoint to each other, to generate the governing equations and inequalities. This procedure was developed by B. Noble and M. J. Sewell (1972) in their study of dual extremum principles in applied mathematics. It is shown that the principles derived here are closely connected to those given by M. Capurso (1972c) for the case of small strains and large displacements. 相似文献
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Nikola Popović Dirk Praetorius Anja Schlömerkemper 《Continuum Mechanics and Thermodynamics》2007,19(1-2):81-109
The analysis of magnetoelastic phenomena is a field of active research. Formulae for the magnetic force in macroscopic systems
have been under discussion for some time. In Popović et al. (Continum. Mech. Thermodyn. 2007), we rigorously justify several
of the available formulae in the context of rigid bodies in two and three space dimensions. In the present, second part of
our study, we investigate these formulae in a series of numerical experiments in which the magnetic force is computed in dependence
on the geometries of the bodies as well as on the distance between them. In case the two bodies are in contact, i.e., in the
limit as their distance tends to zero, we focus especially on a formula obtained in a discrete-to-continuum approximation.
The aim of our study is to help clarify the question which force formula is the correct one in the sense that it describes
nature most accurately and to suggest adequate real-life experiments for a comparison with the provided numerical data.
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We determine the general form of the potential of the problem of motion of a rigid body about a fixed point, which allows the angular velocity to remain permanently in a principal plane of inertia of the body. Explicit solution of the problem of motion is reduced to inversion of a single integral. A several-parameter generalization of the classical case due to Bobylev and Steklov is found. Special cases solvable in elliptic and ultraelliptic functions of time are discussed. 相似文献
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