Reduction,relative equilibria and potential in the two rigid bodies problem   总被引：4，自引：4，他引：0  

Andrzej J. Maciejewski 《Celestial Mechanics and Dynamical Astronomy》1995,63(1):1-28

In this paper the problem of two, and thus, after a generalization, of an arbitrary finite number, of rigid bodies is considered. We show that the Newton-Euler equations of motion are Hamiltonian with respect to a certain non-canonical structure. The system possesses natural symmetries. Using them we shown how to perform reduction of the number of degrees of freedom. We prove that on every stage of this process equations of motion are Hamiltonian and we give explicite form corresponding of non-canonical Poisson bracket. We also discuss practical consequences of the reduction. We prove the existence of 36 non-Lagrangean relative equilibria for two generic rigid bodies. Finally, we demonstrate that our approach allows to simplify the general form of the mutual potential of two rigid bodies.  相似文献   

Exact analytic solution for the rotation of a rigid body having spherical ellipsoid of inertia and subjected to a constant torque     

Marcello Romano 《Celestial Mechanics and Dynamical Astronomy》2008,100(3):181-189

The exact analytic solution is introduced for the rotational motion of a rigid body having three equal principal moments of inertia and subjected to an external torque vector which is constant for an observer fixed with the body, and to arbitrary initial angular velocity. In the paper a parametrization of the rotation by three complex numbers is used. In particular, the rows of the rotation matrix are seen as elements of the unit sphere and projected, by stereographic projection, onto points on the complex plane. In this representation, the kinematic differential equation reduces to an equation of Riccati type, which is solved through appropriate choices of substitutions, thereby yielding an analytic solution in terms of confluent hypergeometric functions. The rotation matrix is recovered from the three complex rotation variables by inverse stereographic map. The results of a numerical experiment confirming the exactness of the analytic solution are reported. The newly found analytic solution is valid for any motion time length and rotation amplitude. The present paper adds a further element to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.  相似文献   

On the rocking–sliding instability of rigid blocks under ground excitation: Some new findings     

《Soil Dynamics and Earthquake Engineering》2015

Rocking (overturning) instability analyses of rigid blocks based on the assumption that the friction between the block and the ground is sufficiently large to exclude the effect of sliding, are reconsidered by including the effect in question. Both modes of overturning instability – without impact and after one impact – are thoroughly discussed in connection with small sliding, whose value depends on the values of kinetic (dry) friction coefficient and the external frequency excitation. Using an energy approach the analytical derivation of the nonlinear differential equations of motion of free-standing rigid blocks under one-sine ground pulse including the effect of sliding, are comprehensively established. The serious difficulties in solving this problem on one hand the change of the kinetic friction coefficient during the motion and on the other hand the reliable evaluation of the actual friction effect when rocking is included, are effectively confronted. This is achieved through a reliable approximation of an equivalent (reduced) coefficient assuming that the major part of friction takes place from the initiation of motion and terminates shortly after the onset of rocking. In cases of slender blocks closed form solutions for overturning due to simultaneous rocking–sliding without or after one impact, are conveniently derived. Among other findings, it was explored that the single block in question for small values of the external frequency (long periods of excitation) the sliding effect is beneficial (stabilizing the block), while for large values of external frequency this effect is detrimental (destabilizing the block).  相似文献   

Numerical study of excavation induced fractures using an extended rigid block spring method     

《Computers and Geotechnics》2017

This paper presents a numerical study of fracturing process induced by excavation around a gallery using an extended rigid block spring method (RBSM). The surrounding rock mass is characterized by an assembly of rigid blocks based on a degraded Voronoi diagram. The macroscopic mechanical behavior of rock is related to that of interfaces between blocks. The mechanical behavior of each interface is described by its elastic stiffness and failure criterion. The failure process of interface is controlled by both normal stress and shear stress. Both tensile and shear failures are considered. The macroscopic fracturing process is described by the coalescence of cracked interfaces. The rock structural anisotropy is taken into account through a spatial variation of elastic stiffness and failure strength of interfaces. A series of sensitivity studies are performed to investigate effects of gallery orientation, failure strength of interfaces and rock structural anisotropy on gallery deformation and fracturing. Numerical results are compared with in-situ observations in terms of fracture patterns.  相似文献   

波浪条件下刚性植被茎干紊流对沉积物再悬浮的促进作用     

易雨君  唐彩红  张尚弘 《湖泊科学》2020,32(6):1827-1836

浅水湖泊沉积物再悬浮过程促进了沉积物内源性物质的释放,造成湖泊水体内源污染,加剧湖泊水质污染与生态恶化.开展刚性植被不同分布格局下的沉积物再悬浮水槽试验,能为浅水草型湖泊、滨海湿地等水环境治理与生态修复提供理论参考.本研究通过开展实验室波浪水槽试验,检验了3种直径12种密度的刚性模型植被对波浪扰动白洋淀沉积物再悬浮的影响,通过测定不同植被情景不同波浪条件下的瞬时速度和沉积物再悬浮浓度,详细阐述了植被产生的紊动能对沉积物再悬浮临界状态的影响,构建并验证了沉积物再悬浮植被紊流模型,预测了沉积物再悬浮的临界速度,为湿地生态恢复与保护提供参考.结果表明：1）植被的存在能有效增加近床面的紊动能;2）紊动能是控制沉积物再悬浮的关键性因素;3）沉积物再悬浮的临界波速与植被的固相体积分数相关.  相似文献