Rigid Body Dynamics Borisov, Alexey; Mamaev, Ivan S; Higher Education Press Ltd. Comp., Higher Education
2018, 2018-12-03, Letnik:
52
eBook
This book provides an up-to-date overview of results in rigid body dynamics, including material concerned with the analysis of nonintegrability and chaotic behavior in various related problems. The ...wealth of topics covered makes it a practical reference for researchers and graduate students in mathematics, physics and mechanics. Contents Rigid Body Equations of Motion and Their Integration The Euler - Poisson Equations and Their Generalizations The Kirchhoff Equations and Related Problems of Rigid Body Dynamics Linear Integrals and Reduction Generalizations of Integrability Cases. Explicit Integration Periodic Solutions, Nonintegrability, and Transition to Chaos Appendix A : Derivation of the Kirchhoff, Poincaré - Zhukovskii, and Four-Dimensional Top Equations Appendix B: The Lie Algebra e(4) and Its Orbits Appendix C: Quaternion Equations and L-A Pair for the Generalized Goryachev - Chaplygin Top Appendix D: The Hess Case and Quantization of the Rotation Number Appendix E: Ferromagnetic Dynamics in a Magnetic Field Appendix F: The Landau - Lifshitz Equation, Discrete Systems, and the Neumann Problem Appendix G: Dynamics of Tops and Material Points on Spheres and Ellipsoids Appendix H: On the Motion of a Heavy Rigid Body in an Ideal Fluid with Circulation Appendix I: The Hamiltonian Dynamics of Self-gravitating Fluid and Gas Ellipsoids
Additive manufacturing offers a unique way of anisotropic microstructure control with a high degree of design freedom. This study demonstrates that application of suitable process parameters and ...laser sources in selective laser melting may favour either one sharp single component texture, more uniformly distributed crystal orientation, or a combination of the above in a preferred gradient, which influence the mechanical properties. It is shown that transitions in microstructure, texture, and properties in fabricated Inconel 718 functionally graded components can be obtained at relatively small or large length scales, depending upon the functional gradient desired in a particular application. Results obtained by electron backscatter diffraction showed distinct regions of coarse elongated grains with a strong (001) orientation uniformly embedded in randomly distributed fine grained matrix. Mechanical tests in the form of hardness, tensile and in-situ digital image correlation tests showed steep transitions in the developed Inconel gradients. The observed mechanical properties were found to be primarily dependent on the grain size and texture and are superior to the cast samples for both laser sources. The developed process strategy can be further applied to design functional gradients with selected tailored properties and to account for directional anisotropy of solidified components.
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•The functionally graded Inconel 718 was produced with different regions of fine and coarse grained microstructure.•Areas processed with high power energy showed a strongly textured microstructure and grains elongated in (001) direction.•There is a sharp transition in mechanical properties and microstructure for processed Inconel gradients.•The developed processing strategy shows the feasibility of creating materials with user-defined functional performance.
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Recently, lattice titanium manufactured by additive manufacturing (AM) techniques has been utilized in various applications, including biomedical. The effects of topological design ...and processing parameters on the fatigue behaviour of such meta-biomaterials have been studied before. Most studies show that the fatigue life of additively manufactured lattice structures is limited. Post-processing techniques could play a major role in improving the fatigue of these promising biomaterials. This study aims to provide an in-depth investigation into the effects of heat treatments, hot isostatic pressing (HIP), sand blasting, and chemical etching on the microstructure, surface morphology, strength and fatigue resistance of selective laser melted titanium meta-biomaterials. It was found that the combination of microstructural design and surface engineering, induced by HIP and sand blasting respectively, allows to increase the endurance limit of these lattice meta-biomaterials by a factor of two. HIP treatment substantially decreased the internal porosity and transformed the microstructure to a more ductile mixture of α + β phases. Sand blasting allowed to eliminate surface imperfections and induced favourable compressive stress in the surface layer of the struts.
Additively manufactured metallic meta-biomaterials are progressively being used as bone replacement orthopedic implants. While there is a great amount of research related to topological designs and their effect on mechanical (e.g. stiffness), physical (e.g. mass transport), and biological (e.g. osseointegration) properties, fatigue lifetime of such structures remains limited. This study provides fundamental investigation into the combined effect of microstructural design and surface engineering of titanium meta-biomaterial, enabled through various post treatment methods ranging from heat treatments to physical and chemical surface modifications. The findings show that fatigue life is significantly improved by applying developed herein novel method, which effortlessly can be used on other bone-mimicking metallic meta-biomaterials.
The electromagnetic radiation of an electron in a constant background tensor field that violates Lorentz invariance is investigated in the framework of the Standard Model Extension. It is shown that ...the radiation effect can manifest itself under astrophysical conditions at ultrahigh electron energy.
This paper is concerned with a nonholonomic system with parametric excitation-the Chaplygin sleigh with time-varying mass distribution. A detailed analysis is made of the problem of the existence of ...regimes with unbounded growth of energy (an analogue of Fermi's acceleration) in the case where excitation is achieved by means of a rotor with variable angular momentum. The existence of trajectories for which the translational velocity of the sleigh increases indefinitely and has the asymptotics is proved. In addition, it is shown that, when viscous friction with a nondegenerate Rayleigh function is added, unbounded speed-up disappears and the trajectories of the reduced system asymptotically tend to a limit cycle.
On inhomogeneous nonholonomic Bilimovich system Borisov, A.V.; Tsiganov, A.V.; Mikishanina, E.A.
Communications in nonlinear science & numerical simulation,
March 2021, 2021-03-00, 20210301, Letnik:
94
Journal Article
Recenzirano
•We study time-dependent non Hamiltonian deformations of the Euler equations describing free motion of the rigid body.•Inhomogeneous Bilimovich’s constraint allows us to reduce this system to ...periodically forced nonautonomous equations.•Poincare map method is applied to study multiscale temporal dynamics of these nonautonomous differential equations.•One gets various equilibrium points, attractors and strange attractors, compact and noncompact attractive curves and calculates their Lyapunov characteristics.•We discuss possibility to control this nonholonomic system via parameters of the constraint.
We consider a simple motivating example of a non-Hamiltonian dynamical system with time-dependent constraints obtained by imposing rheonomic non-integrable Bilimovich’s constraint on a freely rotating rigid body. Dynamics of this low-dimensional nonlinear nonautonomous dynamic system involves different kinds of stable and unstable attractors, quasi and strange attractors, compact and noncompact invariant attractive curves, etc. To study this cautionary example we apply the Poincaré map method to disambiguate and discover multiscale temporal dynamics, specifically the coarse-grained dynamics resulting from fast-scale nonlinear control via nonholonomic Bilimovich’s constraint.
We study the implementation of the optimal control strategy obtained in
1
and supplemented in
2
. The algorithm for optimal stabilization of a linear stochastic differential system in a position ...determined by a piecewise constant Markov drift has been tested in a substantial number of model experiments. The drift value is observed indirectly; i.e., the control problem is solved in the statement with incomplete information. Practical implementation is complicated by the instability of Euler–Maruyama numerical schemes that implement the Wonham filter, which is a key element of the optimal control strategy. To perform calculations, the Wonham filter is approximated by stable schemes based on the optimal filtering of Markov chains by discretized observations
3
. These schemes have different implementation complexity and orders of accuracy. The paper presents a comparative analysis of the control performance for various stable approximations to the Wonham filter and its typical implementation using the Euler–Maruyama scheme. In addition, three versions of discretized filters are compared and final recommendations are given for their application in the problem of stabilizing a system with hopping drift.
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The paper proposes a method of intellectual support for the adoption of logistics decisions on the basis of genetic clustering and fuzzy modeling. The task was set and the solution of the ...interrelated tasks of dividing the territory of logistics services into zones, determining the required number of vehicles in the distribution of logistics orders by zones, and the assignment of vehicles for the implementation of logistics orders was presented. The use of the proposed method (by the example of online vehicle orders) makes it possible to improve the quality and efficiency of the logistics decisions.
The present paper is a continuation of the series of articles
1
,
2
and is devoted to solving the problem of estimating the parameters of hidden Markov models. The hidden state is a homogeneous ...Markov jump process with a finite set of states. The available observations are indirect and contain Wiener processes whose intensities are different and depend on the hidden state. Both the intensity matrix of Markov state transitions and the drift and diffusion parameters of the observations are subject to estimation. For identification, an iterative algorithm based on smoothing the state of the system based on observations over a fixed time interval is proposed. Then, according to these estimates, the parameters are reconstructed. The paper describes in detail all the numerical schemes for estimating the state and for identifying the parameters. A set of illustrative numerical examples is presented, demonstrating the high quality of the proposed identification estimates.
Protons and helium nuclei are the most abundant components of the cosmic radiation. Precise measurements of their fluxes are needed to understand the acceleration and subsequent propagation of cosmic ...rays in our Galaxy. We report precision measurements of the proton and helium spectra in the rigidity range 1 gigavolt to 1.2 teravolts performed by the satellite-borne experiment PAMELA (payload for antimatter matter exploration and light-nuclei astrophysics). We find that the spectral shapes of these two species are different and cannot be described well by a single power law. These data challenge the current paradigm of cosmic-ray acceleration in supernova remnants followed by diffusive propagation in the Galaxy. More complex processes of acceleration and propagation of cosmic rays are required to explain the spectral structures observed in our data.
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