Analysis of chaotic instabilities in a rotating body with internal energy dissipation

Melnikov's method is used to analytically predict the onset of chaotic instability in a rotating body with internal energy dissipation. The model has been found to exhibit chaotic instability when a harmonic disturbance torque is applied to the system for a range of forcing amplitude and frequency. Such a model may be considered to be representative of the dynamical behavior of a number of physical systems such as a spinning spacecraft. In spacecraft, disturbance torques may arise under malfunction of the control system, from an unbalanced rotor, from vibrations in appendages or from orbital variations. Chaotic instabilities arising from such disturbances could introduce uncertainties and irregularities into the motion of the multibody system and consequently could have disastrous effects on its intended operation. A comprehensive stability analysis is performed and regions of nonlinear behavior are identified. Subsequently, the closed form analytical solution for the unperturbed system is obtained in order to identify homoclinic orbits. Melnikov's method is then applied on the system once transformed into Hamiltonian form. The resulting analytical criterion for the onset of chaotic instability is obtained in terms of critical system parameters. The sufficient criterion is shown to be a useful predictor of the phenomenon via comparisons with numerical results. Finally, for the purposes of providing a complete, self-contained investigation of this fundamental system, the control of chaotic instability is demonstated using Lyapunov's method.

Continuous Dependence of Solutions of Quasidifferential Equations with Non-Fixed Time of Impulses

In this article on quasidifferential equation with non-fixed time of impulses we consider the continuous dependence of the solutions on the initial conditions as well as the mappings defined by these equations. We prove general theorems for quasidifferential equations from which follows corresponding results for differential equations, differential inclusion and equations with Hukuhara derivative.

Fixed Point Theorems of Kannan Type for Cyclical Contractive Conditions

The main aim of this paper is to obtain fixed point theorems for Kannan and Zamfirescu operators in the presence of cyclical contractive condition. A method for approximation of the fixed points is also provided, for which both a priori and a posteriori error estimates are given. Our results generalize, unify and extend several important fixed points theorems in literature. In order to illustrate the efficiency of our generalizations five significant examples are also given.

Weak Compatibility and Common Fixed Point Theorems for A-Contractive and E-expansive Maps in Uniform Spaces

2000 Mathematics Subject Classification: 47H10, 54E15.

Some Fixed Point Theorems for Kannan Mappings

2000 Mathematics Subject Classification: Primary: 47H10; Secondary: 54H25.

A Distributed algorithm for 1-D non-linear heat conduction with an unknown point source

Abstract not available

Action Recognition from Motion Capture Data using Meta-cognitive RBF Network Classifier

Action recognition plays an important role in various applications, including smart homes and personal assistive robotics. In this paper, we propose an algorithm for recognizing human actions using motion capture action data. Motion capture data provides accurate three dimensional positions of joints which constitute the human skeleton. We model the movement of the skeletal joints temporally in order to classify the action. The skeleton in each frame of an action sequence is represented as a 129 dimensional vector, of which each component is a 31) angle made by each joint with a fixed point on the skeleton. Finally, the video is represented as a histogram over a codebook obtained from all action sequences. Along with this, the temporal variance of the skeletal joints is used as additional feature. The actions are classified using Meta-Cognitive Radial Basis Function Network (McRBFN) and its Projection Based Learning (PBL) algorithm. We achieve over 97% recognition accuracy on the widely used Berkeley Multimodal Human Action Database (MHAD).

Slightly slanting impact on an elastic cantilever column-an experimental study

Experiments concerning slightly slanting impact between a flat-ended rigid body and a flat-ended elastic cantilever column with a rectangular cross-section have been performed. The experimental results are compared with the theoretical ones. The small angle of incidence was measured by using an optical method. The impact process was studied by using a split disc for the rigid body, with the two halves bonded together and electrically insulated from each other. The disc and the column were parts of an electric circuit. Different contact states could be distinguished according to different voltage levels. Reasonably good agreement between theory and experiment was found. Thus, the impact duration has its minimum under perfectly axial impact as predicted by the theory. Also, the predicted process of alternating line and surface contact was observed. Furthermore, the existence of a small critical angle of incidence was verified. This critical angle of incidence divides the impact processes into two categories: (1) The rigid body and the column end come into surface contact before separation. (2) They separate without surface contact. Comparison of axial strains between theory and experiment shows good agreement.

Análisis Dinámico de mecanismos paralelos con requisitos de diseño mecatrónico

[ES]El objetivo del presente TFG es el Análisis Dinámico de mecanismos paralelos según las necesidades de la mecatrónica. La mecatrónica requiere expresiones explícitas de las fuerzas motoras que sólo dependen de las propias posiciones, velocidades y aceleraciones en los accionamientos. Ello requiere métodos avanzados de la mecánica analítica de sólido rígido. Concretamente se han desarrollado la ecuación de Lagrange modificada (según [11]) y la ecuación de Boltzmann-Hamel modificada, siendo esta última una aportación de este TFG. Como aplicación práctica se ha programado un modelo mecatrónico para un manipulador paralelo 5R y se ha optimizado el diseño de una Multi Axis Simulation Table 3PRS.

立方反射镜失调特性的研究

结合理想坐标系下立方镜镜面微小倾斜后其三个平面法线坐标，利用刚体微量转动的反射法线向量公式，获得非理想立方镜反射矩阵；为了研究在光斜入射时镜面倾斜对出射光方向的影响，利用立方镜绕顶点旋转等效于光斜入射的方法，计算出光束夹角δ与单一镜面偏差角ε和立方镜旋转角θ之间的关系式；对于理想情况下的立方镜，利用几何光学可以证明出射光与入射光不但平行，而且过顶点作任意截面交于两光线所得的两个交点关于顶点对称，从而计算出立方镜绕顶点以外任意轴旋转造成出射光束相对原出射光的偏移量与旋转角关系式，理论计算值与实验数据吻合得很

A comparative evaluation of functions for partitioning nitrogen and amino acid intake between maintenance and growth in broilers

The results from three types of study with broilers, namely nitrogen (N) balance, bioassays and growth experiments, provided the data used herein. Sets of data on N balance and protein accretion (bioassay studies) were used to assess the ability of the monomolecular equation to describe the relationship between (i) N balance and amino acid (AA) intake and (ii) protein accretion and AA intake. The model estimated the levels of isoleucine, lysine, valine, threonine, methionine, total sulphur AAs and tryptophan resulting in zero balance to be 58, 59, 80, 96, 23, 85 and 32 mg/kg live weight (LW)/day, respectively. These estimates show good agreement with those obtained in previous studies. For the growth experiments, four models, specifically re-parameterized for analysing energy balance data, were evaluated for their ability to determine crude protein (CP) intake at maintenance and efficiency of utilization of CP intake for producing gain. They were: a straight line, two equations representing diminishing returns behaviour (monomolecular and rectangular hyperbola) and one equation describing smooth sigmoidal behaviour with a fixed point of inflexion (Gompertz). The estimates of CP requirement for maintenance and efficiency of utilization of CP intake for producing gain varied from 5.4 to 5.9 g/kg LW/day and 0.60 to 0.76, respectively, depending on the models.

A comparative evaluation of functions for describing the relationship between live-weight gain and metabolizable energy intake in turkeys

The suitability of models specifically re-parameterized for analyzing energy balance data relating metabolizable energy intake to growth rate has recently been investigated in male broilers. In this study, the more adequate of those models was applied to growing turkeys to provide estimates of their energy needs for maintenance and growth. Three functional forms were used. They were: two equations representing diminishing returns behaviour (monomolecular and rectangular hyperbola); and one equation describing smooth sigmoidal behaviour with a fixed point of inflexion (Gompertz). The models estimated the metabolizable energy requirement for maintenance in turkeys to be 359-415 kJ/kg of live-weight/day. The predicted values of average net energy requirement for producing 1 g of gain in live-weight, between 1 and 4 times maintenance, varied from 8.7 to 10.9 kJ. These results and those previously reported for broilers are a basis for accepting the general validity of these models.

Hypersonic stagnation‐point boundary layers with massive blowing in the presence of a magnetic field

The effect of massive blowing rates on the steady laminar hypersonic boundary‐layer flow of an electrically conducting fluid in the stagnation region of an axisymmetric body with an applied magnetic field has been studied. The governing equations have been solved numerically by combining the implicit finite‐difference scheme with the quasi‐linearization technique. It is observed that the effect of massive blowing rates is to remove the viscous layer away from the boundary, whereas the effect of the magnetic field is just the opposite. It is also found that the velocity overshoot increases with blowing rates and also with magnetic field. The effect of the variation of the density‐viscosity product across the boundary layer is strong only when the blowing rate is small, but for the massive blowing rate the effect is negligible.

A Compliant Mechanism Kit with Flexible Beams and Connectors

We present the concept, prototypes, and an optimal design method for a compliant mechanism kit as a parallel to the kits available for rigid-body mechanisms. The kit consists of flexible beams and connectors that can be easily hand-assembled using snap fits. It enables users, using their creativity and mechanics intuition, to quickly realize a compliant mechanism. The mechanisms assembled in this manner accurately capture the essential behavior of the topology, shape, size and material aspects and thereby can lead the way for a real compliant mechanism for practical use. Also described in this paper are the design of the connector to which flexible beams can be added in eight different directions; and prototyping of the spring steel connectors as well as beams using wire-cut electro discharge machining. It is noted in this paper that the concept of the kit also resolves a discrepancy in the finite element (FE) modeling of beam-based compliant mechanisms. The discrepancy arises when two or more beams are joining at one point and thus leading to increased stiffness. After resolving this discrepancy, this work extends the topology optimization to automatically generate designs that can be assembled with the kit. Thus, the kit and the accompanying analysis and optimal synthesis procedures comprise a self-contained educational as well as a research and pragmatic toolset for compliant mechanisms. The paper also illustrates how human creativity finds new ways of using the kit beyond the original intended use and how it is useful even for a novice to design compliant mechanisms.