Classical Kinematics Research Articles

Mechanical constraints on inversion of coseismic geodetic data for fault slip and geometry: Example from InSAR observation of the 6 October 2008Mw6.3 Dangxiong-Yangyi (Tibet) earthquake

[1] Modern geodetic techniques, such as the global positioning system (GPS) and Interferometric Synthetic Aperture Radar (InSAR), provide high-precision deformation measurements of earthquakes. Through elastic models and mathematical optimization methods, the observations can be related to a slip distribution model. The classic linear, kinematic, and static slip inversion problem requires specification of a smoothing norm of slip parameters and a residual norm of the data and a choice about the relative weight between the two norms. Inversions for unknown fault geometry are nonlinear and, therefore, the fault geometry is often assumed to be known for the slip inversion problem. We present a new method to invert simultaneously for fault slip and fault geometry assuming a uniform stress drop over the slipping area of the fault. The method uses a full Bayesian inference method as an engine to estimate the posterior probability distribution of stress drop, fault geometry parameters, and fault slip. We validate the method with a synthetic data set and apply the method to InSAR observations of a moderate-sized normal faulting event, the 6 October 2008 Mw 6.3 Dangxiong-Yangyi (Tibet) earthquake. The results show a 45.0 ± 0.2° west dipping fault with a maximum net slip of ∼1.13 m, and the static stress drop and rake angle are estimated as ∼5.43 MPa and ∼92.5°, respectively. The stress drop estimate falls within the typical range of earthquake stress drops known from previous studies.

Gradient Plasticity for Single Crystals

AbstractThe kinematic relationship between classical single crystal kinematics and geometrically necessary dislocations will be clarified by a demonstrative example. The starting point for the dynamics is the contribution of geometrically necessary dislocations to the free energy, which leads to a kinematic hardening law. A simple two‐dimensional shear example will be discussed. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Exploring students' understanding of reference frames and time in Galilean and special relativity

This paper aims at exploring prospective physics teachers' reasoning associated with the concepts of reference frame, time and event which form the framework of the classical kinematics and that of the relativistic kinematics. About 100 prospective physics teachers were surveyed by means of a questionnaire involving classical kinematics situations and relativistic ones. The analysis of the answers shows a deep lack of understanding of both concepts of reference frame and event. Some students think that events may be simultaneous for an observer and not simultaneous for another one, even when both observers are located in the same reference frame. Most of the students surveyed cannot give an answer only depending on the location of the observer when his/her velocity is mentioned as if the movement contaminated the event. This lack of understanding is embodied in reasoning implemented by the population surveyed to address classical kinematics questions and seems to form a major obstacle to grasping relativistic kinematics.

A kinematical approach to gravitational lensing using new formulae for refractive index and acceleration

This paper uses the Schwarzschild metric to derive an effective refractive index and acceleration vector that account for relativistic deflection of light rays, in an otherwise classical kinematic framework. The new refractive index and the known path equation are integrated to give accurate results for travel time and deflection angle, respectively. A new formula for coordinate acceleration is derived which describes the path of a massless test particle in the vicinity of a spherically symmetric mass density distribution. A standard ray-shooting technique is used to compare the deflection angle and time delay predicted by this new formula with the previously calculated values, and with standard first order approximations. Finally, the ray shooting method is used in theoretical examples of strong and weak lensing, reproducing known observer-plane caustic patterns for multiple masses.

Classical kinematics for Lorentz violation

Classical point-particle relativistic lagrangians are constructed that generate the momentum–velocity and dispersion relations for quantum wave packets in Lorentz-violating effective field theory.

Spacecraft aerodynamics and trajectory simulation during aerobraking

This paper uses a direct simulation Monte Carlo (DSMC) approach to simulate rarefied aerodynamic characteristics during the aerobraking process of the NASA Mars Global Surveyor (MGS) spacecraft. The research focuses on the flowfield and aerodynamic characteristics distribution under various free stream densities. The variation regularity of aerodynamic coefficients is analyzed. The paper also develops an aerodynamics-aeroheating-trajectory integrative simulation model to preliminarily calculate the aerobraking orbit transfer by combining the DSMC technique and the classical kinematics theory. The results show that the effect of the planetary atmospheric density, the spacecraft yaw, and the pitch attitudes on the spacecraft aerodynamics is significant. The numerical results are in good agreement with the existing results reported in the literature. The aerodynamics-aeroheating-trajectory integrative simulation model can simulate the orbit transfer in the complete aerobraking mission. The current results of the spacecraft trajectory show that the aerobraking maneuvers have good performance of attitude control.

Planning foot placements for a humanoid robot: A problem of inverse kinematics

We present a novel approach to plan foot placements for a humanoid robot according to kinematic tasks. In this approach, the foot placements are determined by the continuous deformation of a robot motion including a locomotion phase according to the desired tasks. We propose to represent the motion by a virtual kinematic tree composed of a kinematic model of the robot and articulated foot placements. This representation allows us to formulate the motion deformation problem as a classical inverse kinematics problem on a kinematic tree. We first provide details of the basic scheme where the number of footsteps is given in advance and illustrate it with scenarios on the robot HRP-2. Then we propose a general criterion and an algorithm to adapt the number of footsteps progressively to the kinematic goal. The limits and possible extensions of this approach are discussed last.

Auto-detection micro-controller-based autonomous band wrapping system for targeted pest control

With a view toward enhancing pest control and achieving organic requirements in wine industry, development of a prototypical autonomous vehicle that automatically applies a band barrier on grapevine is detailed in this paper. A novel band wrapper mechanism is proposed in this work. The band wrapper serving as the carrier for pest control is applied by the vehicle’s six degree-of-freedom articulator real-time controlled through classical inverse kinematics. It is found in the laboratory that the automated band wrapper robot can successfully detect a rod-like object and optimally place the band wrapper on the desired location for pest control.

ROBOT FORMATION MODELLING AND CONTROL BASED ON THE RELATIVE KINEMATICS EQUATIONS

This paper deals with the problem of modeling, initialization, and control of mobile robots formation. We suggest to use a new family of methods that consists of a combination between classical guidance laws and kinematics rules. These methods allow modeling and controlling a dynamic robotic formation using sets of differential equations that give the relative motion between the robots. These differential equations give the range rate and the visibility angle between leaders and followers. Graph theory is used to store the relationship leader-follower and plan the formation by using three different matrices. The configuration of the formation is based on these matrices. Initialization of formation is also considered, where different approaches are suggested. Because of the nature of the kinematics laws, it is easy to model, initialize, and keep any formation shape. Simulation is provided to illustrate the method.

Compressive residual stress induced by water cavitation peening: A finite element analysis

Water cavitation peening is a recent promising method in surface treatment. It has the potential to induce compressive residual stresses that benefit the fatigue life of components similar to the other peening process. In this paper, a novel method, proposed for predicting residual stress induced on the materials subsurface treated with water cavitation peening, is presented. A bilinear elastic–plastic finite element analysis was conducted to predict to residual stresses. The three-dimensional model was based on the classical bilinear kinematic hardening model that uses two slopes (elastic and plastic) to represent the stress–strain behavior of a material. The approach provided prediction of magnitude and depth of residual stress fields in pure titanium. Effect of applied impact pressures on the residual stresses was also presented. Results of the finite element analysis modeling were in good agreement with that of the experimental measurements.

Evolutionary synthesis of kinematic mechanisms

AbstractThis paper discusses the application of genetic programming to the synthesis of compound two-dimensional kinematic mechanisms, and benchmarks the results against one of the classical kinematic challenges of 19th century mechanical design. Considerations for selecting a representation for mechanism design are presented, and a number of human-competitive inventions are shown.

How Animals Work

Molecular biology and advanced techniques informed by chemistry and physics have changed biological research and teaching. Today's students take for granted that as they study the life sciences, they will hear a lot about genes and molecules. Sir William Harvey would be profoundly disorientated and then gratified by a visit to the Harvey Society's website (www.harveysociety.org). The man who accurately described the functional anatomy of the circulatory system would appreciate the extent to which his evidence-based approach to animal physiology has won the day. Indeed, understanding life processes at a molecular level is immensely satisfying. Three cheers for reductionism (Figure 1). Figure 1. The i heart guts website sells plush toys based on most of your favorite internal organs. It can be difficult, however, to fully appreciate the beauty of molecular details if the larger functions they serve are poorly understood. After all, it is the anatomical genius of the circulatory system that ensures that every cell of the body benefits from the marvel of hemoglobin. The steadily growing body of biological information makes it more challenging to preserve places in the curriculum to provide organismal and physiological context for students, and to cultivate deep thinking about how complex biological systems function through emergent properties of molecular mechanics. We are all interested in how our bodies work and are obsessed, if not enthralled, by our innards, or as one website (http://iheartguts.com/) would put it, “we heart guts.” My main goal for this review is to uncover websites that can be used to infuse the biology curriculum with systems and organismal context. Because a human anatomy and physiology (A&P) sequence is still part of most life science curricula, websites that support the teaching of A&P vastly outnumber websites concerned with general physiological principles or comparative physiology and anatomy. I highlight websites that emphasize fundamental principles and a comparative approach, but I also point to several excellent sites devoted to human A&P (Figure 2). Figure 2. The University of Utah Medical Library has a number of outstanding educational resources and tutorials on its Knowledge Weavers website, including an excellent animation of the circulation through the heart. To honor Harvey, let's begin by looking at a website that does an outstanding job of showing how our hearts work. The Knowledge Weavers website (http://library.med.utah.edu/kw/) from the University of Utah medical library offers many excellent resources. Their Flash-animated heart (http://library.med.utah.edu/kw/resources.html#animations) is one of the best of many available on the Web. The action of the heart is linked to dynamic graphs of blood pressure/volume, electrocardiogram, and heart sounds. The progress of the heart cycle is tracked by systole and diastole, in turn subdivided into relevant phases, and controls are available to run the animation fast, slow, or in step-through mode. The Flash console conveniently locates links to tutorials. The tutorials, by dissecting the animation step by step, should help students consolidate their learning based on the animation. It would be an interesting assessment to have students make their own tutorials and then see how they measure up to those made by the website authors. In addition to the cardiology information, the site also has an interesting concept for presenting a functional neural pathway. The Osteointeractive section (http://library.med.utah.edu/kw/osteo/index2.html) is noteworthy in presenting topics such as forensic anthropology and paleopathology, including the use of bones for human rights work. They've also developed tools to help faculty make multimedia and Web-based quizzes.

Classical and non-classical kinematic fields of two-dimensional penetration tests on granular ground by discrete element method analyses

The penetration test is a widely used in-situ test in geotechnical engineering which mechanism is very important to geomechanics. This paper presents a numerical study on both classic and non-classic kinematic fields in penetration tests on granular ground. A two-dimensional Discrete Element Method (DEM) has been used to simulate penetration tests on a full-size granular ground that is under an amplified gravity and under a K 0 lateral stress boundary. In addition to classical kinematic variables, i.e. displacement and velocity, a non-classical kinematic variable called the average pure rotation rate (APR), which represents particle sizes and particle rotations (M. J. Jiang et al. Kinematic models for non-coaxial granular materials: Part I: theories. Int J Numer Anal Methods Geomech 2005; 29(7): 643–661), is investigated in the penetration test. The DEM numerical results show that the penetration leads to significant changes in displacement, velocity and APR fields, making the soil near the penetrometer move in complex displacement and APR paths. In comparison to velocity field, APR field is very ‘localized’ in the area close to the penetrometer shoulder during penetration. Based on the normalized tip resistance, the penetration process can be described by three phases of penetration, in which the granular ground undergoes three types of failure mechanism, respectively.

Dynamic time warping: A new method in the study of poor handwriting

Poor handwriting is a diagnostic criterion for developmental coordination disorder. Typical of poor handwriting is its low overall quality and the high variability of the spatial characteristics of the letters, usually assessed with a subjective handwriting scale. Recently, Dynamic Time Warping (DTW), a technique originally developed for speech recognition, was introduced for pattern recognition in handwriting. The present study evaluates its application to analyze poor handwriting. Forty children attending Dutch mainstream primary schools were recruited and based on their scores on the Concise Evaluation Scale for Children’s Handwriting (Dutch abbreviation: BHK), 20 good and 20 poor writers (of whom 13 were scheduled for handwriting intervention) were identified. The groups were matched for age (7–9 years), school grade (grades 2 and 3) and handedness. The children subsequently wrote sequences of the letter “a” on a graphics tablet in three conditions (normal, fast, and accurate). Classical kinematics were obtained and for each individual letter DTW was used to calculate the distance from the mean shape. The DTW data revealed much higher variability in the letter forms of the poor writers that was independent of the kinematic results of larger trajectories, faster movements, and higher pen pressure. The current results suggest that DTW is a valid and objective technique for letter-form analysis in handwriting and may hence be useful to evaluate the rehabilitation treatments of children suffering from poor handwriting. In education research it may be exploited to explore how children (should) learn to write.

Doppler effect in Schwarzschild and Kerr geometries

Calculation of the Doppler shift in general relativity involves contributions of gravitational and kinematical origins and for most metrics or trajectories these contributions are coupled. The exact expression for this Doppler shift may simplify for particular symmetries. Here the specific case for a light signal emitted by a distant inertial observer and received by an in-falling observer in a Schwarzschild geometry is discussed. The resulting expression the Doppler shift is composed of simple factors that can be clearly identified with contributions arising from classical kinematical, special relativistic and general relativistic origins. This result turns out to be more general and it holds for a case of an arbitrary radial in-fall in Schwarzschild geometry and for a particular type of in-fall in the case of a Kerr metric.

Kinematic hardening rules for modeling uniaxial and multiaxial ratcheting

Ratcheting, which is the strain accumulation observed under the unsymmetrical stress controlled loading and non-proportional loadings, is modeled using the simplified viscoplasticity theory based on overstress (VBO). The influences of kinematic hardening laws on the uniaxial and multiaxial non-proportional ratcheting behavior of CS 1026 carbon steel have been investigated. The following kinematic hardening rules have been considered: the classical kinematic hardening rule, the kinematic hardening rules introduced by Armstrong–Frederick, Burlet–Cailletaud and the modified Burlet–Cailletaud. The investigated loading conditions include uniaxial stress controlled test with non-zero mean stress, and axial strain controlled cyclic test of thin-walled tubular specimen in the presence of constant pressure. Numerical results are compared with the experimental data obtained by Hassan and Kyriakides [Hassan T, Kyriakides S. Ratcheting in cyclic plasticity, part I: uniaxial behavior. Int J Plast 1992;8:91–116] and Hassan et al. [Hassan T, Corona E, Kyriakides S. Ratcheting in cyclic plasticity, part I: multiaxial behavior. Int J Plast 1992;8:117–146]. It is observed that all investigated kinematic hardening rules do not improve ratcheting behavior under multiaxial loading, but over-prediction still exists.

Rolling balls and octonions

In this semi-expository paper we disclose hidden symmetries of a classical nonholonomic kinematic model and try to explain the geometric meaning of the basic invariants of vector distributions.

Deriving Spin within a Discrete-Time Theory

We prove that the classical theory with a discrete time (chronon) is a particular case of a more general theory in which spinning particles are associated with generalized Lagrangians containing time-derivatives of any order (a theory that has been called "Non-Newtonian Mechanics"). As a consequence, we get, for instance, a classical kinematical derivation of Hamiltonian and spin vector for the mentioned chronon theory (e.g., in Caldirola et al.'s formulation).

Age-related differences in the reaching and grasping coordination in children: unimanual and bimanual tasks

This study examined age-related differences in the coordinative mechanism of the reach-to-grasp movement in three groups of children aged 6, 8, and 11 year, and in healthy adults. Three prehension conditions were manipulated: an unimanual and a bimanual self-driven tasks in which the reaching and grasping of the object were performed by participants, and a bimanual externally-driven task, in which the experimenter brought the object into the vicinity of the participant which grasped it. Classical kinematics data-peak velocities of the reaching and the grasping, the time to onset grip opening, maximum grip opening and grip closure-were calculated. Moreover, to obtain equivalent kinematics variables for all age groups, relative time to peak velocity (% of reaching duration), relative maximum grip opening (% of object size), and percentage of the four types of phase plans between reaching velocity and grip size have been calculated for each group of age. Our main results showed (1) a high variability at age 6, (2) an age-related change between the 6- and 8-year old for almost all of the dependent variables, and (3) a significant difference between the 11-year olds and adults. In summary, at 6 years, the interdependence between the reaching and grasping programs was unstable. A transitory feedback-based coordination between reaching and grasping appeared at 8 years of age. Finally, the adults' relationship between reaching and grasping was not attained at the age of 11.

Limit analysis of composite materials based on an ellipsoid yield criterion

Employing repeating unit cell (RUC) to represent the microstructure of periodic composite materials, this paper develops a numerical technique to calculate the plastic limit loads and failure modes of composites by means of homogenization technique and limit analysis in conjunction with the displacement-based finite element method. With the aid of homogenization theory, the classical kinematic limit theorem is generalized to incorporate the microstructure of composites. Using an associated flow rule, the plastic dissipation power for an ellipsoid yield criterion is expressed in terms of the kinematically admissible velocity. Based on nonlinear mathematical programming techniques, the finite element modelling of kinematic limit analysis is then developed as a nonlinear mathematical programming problem subject to only a small number of equality constraints. The objective function corresponds to the plastic dissipation power which is to be minimized and an upper bound to the limit load of a composite is then obtained. The nonlinear formulation has a very small number of constraints and requires much less computational effort than a linear formulation. An effective, direct iterative algorithm is proposed to solve the resulting nonlinear programming problem. The effectiveness and efficiency of the proposed method have been validated by several numerical examples. The proposed method can provide theoretical foundation and serve as a powerful numerical tool for the engineering design of composite materials.