Rigid Body Motion

This paper presents an approach to recognize 6 DOF rigid body motion trajectories (3D translation + rotation), such as the 6 DOF motion trajectory of an object manipulated by a human. As a first step in the recognition process, 3D measured position trajectories of arbitrary and uncalibrated points attached to the rigid body are transformed to an invariant, coordinate-free representation of the rigid body motion trajectory. This invariant representation is independent of the reference frame in which the motion is observed, the chosen marker positions, the linear scale (magnitude) of the motion, the time scale and the velocity profile along the trajectory. Two classification algorithms which use the invariant representation as input are developed and tested experimentally: one approach based on a Dynamic Time Warping algorithm, and one based on Hidden Markov Models. Both approaches yield high recognition rates (up to 95 % and 91 %, respectively). The advantage of the invariant approach is that motion trajectories observed in different contexts (with different reference frames, marker positions, time scales, linear scales, velocity profiles) can be compared and averaged, which allows us to build models from multiple demonstrations observed in different contexts, and use these models to recognize similar motion trajectories in still different contexts.

The Large Synoptic Survey Telescope (LSST) is a three mirror modified Paul-Baker design with an 8.4m primary, a 3.4m secondary, and a 5.0m tertiary followed by a 3-element refractive corrector producing a 3.5 degree field of view. This design produces image diameters of <0.3 arcsecond 80% encircled energy over its full field of view. The image quality of this design is sufficient to ensure that the final images produced by the telescope will be limited by the atmospheric seeing at an excellent astronomical site. In order to maintain this image quality, the deformations and rigid body motions of the three large mirrors must be actively controlled to minimize optical aberrations. By measuring the optical wavefront produced by the telescope at multiple points in the field, mirror deformations and rigid body motions that produce a good optical wavefront across the entire field may be determined. We will describe the details of the techniques for obtaining these solutions. We will show that, for the expected mirror deformations and rigid body misalignments, the solutions that are found using these techniques produce an image quality over the field that is close to optimal. We will discuss how many wavefront sensors are needed and the tradeoffs between the number of wavefront sensors, their layout and noise sensitivity.

We solve the problem of rigid motion in special relativity in completeness, forswearing the use of the 4-D geometrical methods usually associated with relativity, for pedagogical reasons. We eventually reduce the problem to a system of coupled linear nonhomogeneous ordinary differential equations. We find that any rotation of the rigid reference frame must be independent of time. We clarify the issues associated with Bell's notorious rocket paradox and we discuss the problem of hyperbolic motion from multiple viewpoints. We conjecture that any rigid accelerated body must experience regions of shock in which there is a transition to fluid motion, and we discuss the hypothesis that the Schwarzchild surface of a black hole is just such a shock front.

Automatic emotion recognition gained significant importance in the recent decade, especially with the development of artificial intelligence, which has affected our daily lives. Using personalized emotion recognition in healthcare, education, retail, and automotive has high importance these days, which requires proper data in different modalities. On the other hand, data scarcity in some emotion recognition modalities, such as body motion and physiological signals, is vivid, especially when it comes to multimodality. Furthermore, the way a participant is provoked to show emotion is crucial, as it should resemble real-life emotional expression. To do so, one of the most effective methods is to employ Virtual Reality (VR) videos and games. This paper introduces a novel Multimodal Virtual Reality Stimuli-based emotion recognition dataset, or MVRS, which could address the mentioned data scarcity issue. Our dataset contains 13 subjects or participant stimuli using VR videos for relaxation, fear, stress, sadness, and joy emotions. The dataset covers an age range of 12 to 60 in both genders. This dataset is recorded in a small lab in which all participants followed the same data collection protocols and filled out both questionnaires and consent forms. The dataset includes eye tracking, body motion, ElectroMyoGraphy (EMG), and Galvanic Skin Response (GSR) data in various formats. The eye-tracking data is recorded using a Full High-Definition (FHD) webcam placed manually into the VR Head-Mounted Display (HMD). The body motion data is recorded using Microsoft Kinect version 2. Finally, EMG and GSR data are recorded by an Arduino UNO board. All data is recorded simultaneously, with synchronized timestamps, to support clean data for multimodal processing. For each modality, related features are extracted and fused by multimodal fusion techniques (early and late stages) and evaluated using different classifiers and metrics to check the validity and separability of the data.

The goal of this work is to investigate, for a large set of patients, the motion of the heart with respiration during free-breathing supine medical imaging. For this purpose we analyzed the motion of the heart in 32 non-contrast enhanced respiratory-gated 4D-CT datasets acquired during quiet unconstrained breathing. The respiratory-gated CT images covered the cardiac region and were acquired at each of 10 stages of the respiratory cycle, with the first stage being end-inspiration. We devised a 3-D semi-automated segmentation algorithm that segments the heart in the 4D-CT datasets acquired without contrast enhancement for use in estimating respiratory motion of the heart. Our semi-automated segmentation results were compared against interactive hand segmentations of the coronal slices by a cardiologist and a radiologist. The pairwise difference in segmentation among the algorithm and the physicians was on the average 11% and 10% of the total average segmented volume across the patient, with a couple of patients as outliers above the 95% agreement limit. The mean difference among the two physicians was 8% with an outlier above the 95% agreement limit. The 3-D segmentation was an order of magnitude faster than the Physicians' manual segmentation and represents significant reduction of Physicians' time. The segmented first stages of respiration were used in 12 degree-of-freedom (DOF) affine registration to estimate the motion at each subsequent stage of respiration. The registration results from the 32 patients indicate that the translation in the superior-inferior direction was the largest component motion, with a maximum of 10.7 mm, mean of 6.4 mm, and standard deviation of 2.2 mm. Translation in the anterior-posterior direction was the next largest component of motion, with a maximum of 4.0 mm, mean of 1.7 mm, and standard deviation of 1.0 mm. Rotation about the right-left axis was on average the largest component of rotation observed, with a maximum of 4.6 degrees, mean of 1.6 degrees, and standard deviation of 2.1 degrees. The other rotation and shear parameters were all close to zero on average indicting the motion could be reasonably well approximated by rigid-body motion. However, the product of the three scale factors averaged about 0.97 indicating the possibility of a small decrease in heart volume with expiration. The motion results were similar whether we used the Physician's segmentation or the 3-D algorithm.

In the rapidly advancing field of robotics, mathematical tools have become essential for addressing the complex challenges associated with motion analysis and optimization [1-9]. This paper explores the hyper-state of a rigid body in motion, focusing on its position, velocity vector field, and acceleration vector field. It proposes hypercomplex entities representing the hyper-state of motion for rigid bodies and multibody systems. This trident algebra extends dual algebra applied in rigid body kinematics. A differential transform, a symbolic representation that links a real-time function with a trident time function, is the cornerstone of this approach. The analysis employs automatic differentiation through nilpotent trident algebra, eliminating the need for further differentiation concerning time. A proper orthogonal trident tensor and trident unit quaternions encompasses the hyper-state of the rigid body and is an isomorphic homogenous trident matrix. A hyper-state analysis of the general cylindrical spatial chain is presented. The POE quaternionic formula for the hyper-state of lower-pair kinematics chains is demonstrated in compact representation. In the end an application for the hyper-state of a four-degrees-of-freedom general serial 3C manipulator by trident unit quaternions is presented. Moreover, the significant impact of nilpotent algebra extends to automatic differentiation [5], [10], a critical method for achieving accurate computations. This capability is essential for skillfully and precisely navigating complex optimization landscapes.

The paper Borovkova et al. [4] uses the moment matching method to obtain closed form formulas for spread and basket call option prices under log normal models. In this note, we also use the moment matching method to obtain semi-closed form formulas for the price of spread options under exponential Lévy models with mean-variance mixture. Unlike the semi-closed form formula in Caldana and Fusai [5], where spread prices were expressed by using a Fourier inversion formula that involves all the log return processes, our formula gives spread prices in terms of the mixing distribution of the log returns. Numerical tests show that our formulas give accurate spread prices also.

This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The objectives of the project were to develop new mathematical techniques for describing chaotic systems and for reexpressing them in forms that can be solved analytically and computationally. We focused on global bifurcation analysis of rigid body motion in an ideal incompressible fluid and on an analytical technique for the exact solution of nonlinear cellular automata. For rigid-body motion, we investigated a new completely integrable partial differential equation (PDE) representing model motion of fronts in nematic crystals and studied perturbations of the integrable PDE. For cellular automata with multiple domain structures, our work has included 1) identification of the associated set of conserved quantitites for each type of domain; 2) use of the conserved quantitites to construct isomorphism between the nonlinear system and a linear template; and 3) use of exact solvability methods to characterize detailed structure of equilibrium states and to derive bounds for maximal transience times.

Sexual orientation is the attraction one feels to men, women, or both, while advocacy is any effort or activity geared towards supporting people of diverse sexual orientations to eradicate discrimination within a community. In this paper, a comprehensive mathematical model of sexual orientations with advocacy was developed, and the efficacy of advocacy is analysed. The model divided the population into ten compartments: Males, Females, gays, lesbians, heterosexual males, heterosexual females, bisexual males, bisexual females, recovery centres for males, and recovery centres for females. The positivity, boundedness, equilibria points, and control reproduction numbers were studied. The Routh-Hurwitz criteria were used to assess the local stability of the disease-free equilibrium, the Metzler Matrix method was used to determine global stability, while Lyapunov functions were used to study the global stability of the endemic equilibrium point. Bifurcation analysis was also conducted. Lastly, a sensitivity analysis and numerical simulations were conducted using Wolfram Mathematica and MATLAB software. Numerical results showed that the model with advocacy increases the gay, lesbian, bisexual male, and bisexual female populations by 5.7%, 15.6%, 2.6%, and 15.3%, respectively, compared with the model without advocacy. In conclusion, the study showed that while incorporating advocacy in the community significantly increased homosexual populations in the society, Lesbian and bisexual female populations were increased the most.

In this paper, we present an iterative steering algorithm for nonholonomic systems (also called driftless control-affine systems) and we prove its global convergence under the sole assumption that the Lie Algebraic Rank Condition (LARC) holds true everywhere. That algorithm is an extension of the one introduced in [21] for regular systems. The first novelty here consists in the explicit algebraic construction, starting from the original control system, of a lifted control system which is regular. The second contribution of the paper is an exact motion planning method for nilpotent systems, which makes use of sinusoidal control laws and which is a generalization of the algorithm described in for chained-form systems.

We present here the generic parallel computational framework in C++ called Feel++ for the mortar finite element method with the arbitrary number of subdomain partitions in 2D and 3D. An iterative method with block-diagonal preconditioners is used for solving the algebraic saddle-point problem arising from the finite element discretization. Finally we present a scalability study and the numerical results obtained using Feel++ library.

The asymptotic accuracies of structural shell theories are reviewed. Several finite element models to solve arch problems are formulated by utilizing the shell theories. The asymptotic rate of energy convergence is determined by the ability of the approximate strains to assume arbitray polynomial states. The optimal choice of interpolation functions for tangential and normal displacement is treated. Stress resultants and stress couples are evaluated by using nodal forces (strain integration method) or internal strain patterns (strain method). The accuracy of these methods are investigated. In particular the distribution of errors in the strains calculated by the strain method is determined and utilized for accuracte stress evaluation. The theoreticat considerations are supported by a vaste number of numerical experiments, which confirm the theoretical results. * dw/ds is utilized for the w-field. Instead of using the parameter du/ds for the u-field, an additional transformation is performed to have es (cfr. Table la) as parameter.

The asymptotic accuracies of structural shell theories are reviewed. Several finite element models to solve arch problems are formulated by utilizing the shell theories. The asymptotic rate of energy convergence is determined by the ability of the approximate strains to assume arbitray polynomial states. The optimal choice of interpolation functions for tangential and normal displacement is treated. Stress resultants and stress couples are evaluated by using nodal forces (strain integration method) or internal strain patterns (strain method). The accuracy of these methods are investigated. In particular the distribution of errors in the strains calculated by the strain method is determined and utilized for accuracte stress evaluation. The theoreticat considerations are supported by a vaste number of numerical experiments, which confirm the theoretical results. * dw/ds is utilized for the w-field. Instead of using the parameter du/ds for the u-field, an additional transformation is performed to have es (cfr. Table la) as parameter.

 ñîîáùåíèè äëÿ óðàâíåíèÿD ïîëó÷åííîãî èòåðèðîâàíèåì îáûêíîE âåííîãî äèôôåðåíöèàëüíîãî îïåðàòîðà ïåðâîãî ïîðÿäêà ñ òðåìÿ ñëàáî ñèíãóëÿðíûìè òî÷êàìèD íàéäåíî ïðåäñòàâëåíèå îáùåãî ðåE øåíèÿD êîòîðîå ïðèìåíÿåòñÿ äëÿ èññëåäîâàíèÿ ñâîéñòâ ðåøåíèéD âûÿñíåíèÿ ïîñòàíîâêè è ðåøåíèÿ çàäà÷ Êîøè E Ðèêüå è òèïà ëèE íåéíîãî ñîïðÿaeåíèÿF Êëþ÷åâûå ñëîâàX äèôôåðåíöèàëüíîå óðàâíåíèå ñïåöèàëüíîãî òèE ïàD ñëàáî ñèíãóëÿðíàÿ òî÷êàD îáùåå ðåøåíèåD ôîðìóëû îáðàùåíèÿD ñâîéñòâà ðåøåíèéD çàäà÷è Êîøè E Ðèêüå è ëèíåéíîãî ñîïðÿaeåíèÿF Integral representation of the general solution and boundary value problems for an ordinary differential equation of a special type with three weakly singular points In the message for the equation obtained by iterating an ordinary first-order differential operator with three weakly singular points is found representation of the general solution, which is used to study the properties of solutions, formulation and solv of Cauchy -Riquier and linear conjugation problems.

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

The aim of this paper is to establish unified integrals that encompass a diverse set of elements, including multivariable general class of polynomials, Jacobi polynomials, and the I-function of two variables. Initially, we computed integrals involving multivariable general class of polynomials and the I-function of two variables using the Oberhettinger formula. Subsequently, we derived integrals involving Jacobi polynomials and the I-function of two variables. Due to the general nature of I-function of two variables, we also derived specific integrals involving the I-function and the H-function of one variable as special cases based on our primary findings.

A major limitations for many heat engines is that their functioning demands on-line control, and/or an external fitting between environmental parameters (e.g. temperatures of thermal baths) and internal parameters of the engine. We study a model for an adaptive heat engine, where-due to feedback from the functional part-the engine's structure adapts to given thermal baths. Hence no on-line control and no external fitting are needed. The engine can employ unknown resources; it can also adapt to results of its own functioning that makes the bath temperatures closer. We determine thermodynamic costs of adaptation and relate them to the prior information available about the environment. We also discuss informational constraints on the structure-function interaction that are necessary for adaptation.

A contact problem is called tangential when arbitrary tangential displacements are prescribed over a part of the boundary of a transversely isotropic layer, while the tangential stress is zero over the rest of the boundary; the normal stress vanishes all over the boundary. The Generalized Images method is used to give a complete elementary solution to the problem. A new governing integral equation is derived. A particular case of a circular domain of contact is studied in detail. The governing integral equation can be inverted in this case. Approximate formulae are derived for the resultant force and the torque. A direct relationship is established between the integral transform method and the Generalized Images method. A limiting case of general solution gives the solution for an isotropic layer.

The internal space for a molecule, atom, or other n-body system can be conveniently parameterised by 3n -9 kinematic angles and three kinematic invariants. For a fixed set of kinematic invariants, the kinematic angles parameterise a subspace, called a kinematic orbit, of the n-body internal space. Building on an earlier analysis of the three-and four-body problems, we derive the form of these kinematic orbits (that is, their topology) for the general nbody problem. The case n = 5 is studied in detail, along with the previously studied cases n = 3, 4.

The azimuthal Zernike coefficients for shells of Zernike functions with shell numbers n<N may be determined by making measurements at N equally spaced rotational positions. However, these measurements do not determine the coefficients of any of the purely radial Zernike functions. Label the circle that the azimuthal Zernikes are measured in as circle A. Suppose that the azimuthal Zernike coefficients for n<N are also measured in a smaller circle B which is inside circle A but offset so that it is tangent to circle A and so that it has the center of circle A just inside its circular boundary. The diameter of circle B is thus only slightly larger than half the diameter of circle A. From these two sets of measurements, all the Zernike coefficients may be determined for n<N. However, there are usually unknown small rigid body motions of the optic between measurements. Then all the Zernike coefficients for n<N except for piston, tilts, and focus may be determined. We describe the exact mathematical algorithm that does this and describe an interferometer which measures the complete wavefront from pinholes in pinhole aligners. These pinhole aligners are self-contained units which include a fiber optic, focusing optics, and a "pinhole mirror". These pinhole aligners can then be used in another interferometer so that its errors would then be known. Physically, the measurements in circles A and B are accomplished by rotating each pinhole aligner about an aligned axis, then about an oblique axis. Absolute measurement accuracies better than 0.2 nm were achieved.

В данной работе вводится функциональная геометрия (ФГ) — новая самодостаточная геометрическая структура, основанная на эволюции локальных осей X(t) и интегральной синхронизации, без априорного задания метрического тензора или связей. В отличие от традиционного «сверху-вниз» подхода римановой геометрии, в ФГ геометрическая структура возникает снизу-вверх: локальные направления (оси) являются первичными, а метрика и кривизна — их следствиями. Через интегральное уравнение синхронизации и динамическую нормировку достигается глобальная гладкость, аналитическая состоятельность и высокая устойчивость к шуму и локальным флуктуациям, что критично для приложений к инверсным задачам, физике и численной геометрии.

ФГ допускает работу с несимметричными матрицами X(t), тем самым естественным образом порождая торсионную геометрию без необходимости вводить её вручную, как в формализме Картана. Использование гладкого SVD позволяет построить ортонормированные базисы в касательном пространстве без обращения к символам Кристоффеля. Более того, вся геометрия (метрика, кривизна, геодезические) воспроизводится через дифференцирование осей и их интегральные характеристики, не прибегая к ковариантному дифференцированию. В этом смысле ФГ является интуитивной, численно реализуемой и концептуально простой альтернативой классическим формализмам.

Формализм расширяется на комплексные и некоммутативные структуры, включая построение спектрального триплета (A, H, D) и Kähler-инвариантов, что открывает путь к приложениям в квантовой геометрии. В приложениях ФГ демонстрирует устойчивость и точность при восстановлении геометрии из ограниченных или шумовых данных (например, в сейсмической томографии, восстановлении скоростей пласта и компьютерной графике). Численные эксперименты на S², CP¹ и реальных физических данных подтверждают второй порядок сходимости и превосходство метода по сравнению с традиционными схемами.

Функциональная геометрия — это геометрия без предпосылок. Она не требует предварительного задания метрики, а синтезирует геометрическую структуру из эволюции координатной системы, подобно тому как физическое пространство порождается движением. Это делает её универсальным инструментом для как фундаментального анализа, так и прикладной реконструкции сложных пространств.

In the city of Glendora (California, USA) a distinguished scientist, one of the leaders of mathematics in Armenia, the outstanding authority in the theory of the partial differential equations Nazareth Ervandovich Tovmasyan on July, 23rd, 2010 has passed away. N.E. Tovmasyan was born in 1934 in the village Bjni of Hrazdan region of Armenia. In 1951 he entered the physical and mathematical faculty of the Yerevan state university and in 1956 he graduated. N. E. Tovmasyan's scientific activity has begun since that year. In 1956 he started his working career in the Institute of mathematics and mechanics of Academy of Sciences of Armenia. The first Armenian academician-mathematician-A.L. Shahinyan, who those years was the director of the institute, noticed something in new junior research fellow and in 1959, aiming the development the theory of the differential equations in Armenia , sends N.E.Tovmasyan to postgraduate studies in the Steklov Institute of mathematics and mechanics of the Academy of Sciences of the USSR. The supervisor of N. E. Tovmasyan's studies becames the world famous scientist Ilya Nestorovich Vekua. A year later I. N. Vekua has been appointed to the rector position of recently organized university of the Siberian Branch of the Academy of sciences of the USSR, and N. E. Tovmasyan moved with him in the city of Novosibirsk and continued his postgraduate studies in the Institute of hydrodynamics of the Siberian Branch of Academy of Sciences of the USSR. Further, almost ten years' period of the life in Novosibirsk, in the famous Academgorodok, where many glorious pages were added to history of the Soviet science, followed. Those years Tovmasyan worked with M. A. Lavrent'ev, I. N. Vekua, S. L. Sobolev, A. V. Bitzadze and other outstanding Soviet scientists. In 1963 N.E.Tovmasyan completed his PhD thesis and started his work in the Institute of mathematics of the Siberian branch of the Academy of Sciences of the USSR first as junior research fellow, afterwards as senior staff scientist at the division of the theory of functions. In 1967 N.E.Tovmasyan gots his doctor's degree "On the theory of boundary value problems for elliptic systems of the second order." The scientific interests of Nazareth Ervandovich were formed during these years and the basis of his further investigations has been laid. The first works (PhD) are devoted to investigation of Laplace and Tricomi equations in classes of discontinuous functions. Explicit formulas for the solution of the Dirichlet problem for these equations in suitable classes

The axisymmetric and non-axisymmetric motions of a viscoelastic fluid driven by the steady rotations of a pair of coaxial, parallel discs, each of infinite extent, are studied analytically and numerically. The constitutive equation and the equations of motion depend altogether on four parameters and the numerical scheme used is robust and is capable of discovering regular and limit point bifurcations as well as folds arising from the changes in the values of the parameters. First and foremost, the work reported here is an exhaustive collection of old and new results in the above flow problem, including the stability of the axisymmetric flows. Non-existence of bifurcations from the rigid body motion and their appearance from the torsional flow and other flows are found under a variety of conditions, extending from the newtonian to the non-newtonian fluid behaviour. Secondly, the use of a scaling lemma permits the determination of the solutions to the problem over the entire range of ...

Generalized beam-column element on two parameter elastic foundation K. Morfidis, I.E. Avramidis a Dr civil engineer, lecturer, Dept. of Civil Engineering, Division of Structural Engineering, Aristotle University of Thessaloniki 540 06 Thessaloniki b Dr civil engineer, professor, Dept. of Civil Engineering, Division of Structural Engineering, Aristotle University of Thessaloniki, 540 06 Thessaloniki

While coarse-grained (CG) simulations provide an efficient approach to identify small-and largescale motions important to protein conformational transitions, coupling with appropriate experimental validation is essential. Here, by comparing small-angle X-ray scattering (SAXS) predictions from CG simulation ensembles of adenylate kinase (AK) with a range of energetic parameters, we demonstrate that AK is flexible in solution in the absence of ligand and that a small population of the closed form exists without ligand. In addition, by analyzing variation of scattering patterns within CG simulation ensembles, we reveal that rigid-body motion of the LID domain corresponds to a dominant scattering feature. Thus, we have developed a novel approach for three-dimensional structural interpretation of SAXS data. Finally, we demonstrate that the agreement between predicted and experimental SAXS can be improved by increasing the simulation temperature or by computationally mutating selected residues to glycine, both of which perturb LID rigid-body flexibility.

On the basis of intrinsic properties of the vector parameterization of rotational motions this work presents an explicit solution of the problem of decomposition of any finite rotation into a product of three successive finite rotations about prescribed axes.

In this paper, we provide an overview of the adaptive optics (AO) program for the Thirty Meter Telescope (TMT) project, including an update on requirements; the philosophical approach to developing an overall AO system architecture; the recently completed conceptual designs for facility and instrument AO systems; anticipated first light capabilities and upgrade options; and the hardware, software, and controls interfaces with the remainder of the observatory. Supporting work in AO component development, lab and field tests, and simulation and analysis is also discussed. Further detail on all of these subjects may be found in additional papers in this conference.

In the domain of emotion recognition using body motion, the primary challenge lies in the scarcity of diverse and generalizable datasets. Automatic emotion recognition uses machine learning and artificial intelligence techniques to recognize a person's emotional state from various data types, such as text, images, sound, and body motion. Body motion poses unique challenges as many factors, such as age, gender, ethnicity, personality, and illness, affect its appearance, leading to a lack of diverse and robust datasets specifically for emotion recognition. To address this, employing Synthetic Data Generation (SDG) methods, such as Generative Adversarial Networks (GANs) and Variational Auto Encoders (VAEs), offers potential solutions, though these methods are often complex. This research introduces a novel application of the Neural Gas Network (NGN) algorithm for synthesizing body motion data and optimizing diversity and generation speed. By learning skeletal structure topology, the NGN fits the neurons or gas particles on body joints. Generated gas particles, which form the skeletal structure later on, will be used to synthesize the new body posture. By attaching body postures over frames, the final synthetic body motion appears. We compared our generated dataset against others generated by GANs, VAEs, and another benchmark algorithm, using benchmark metrics such as Fréchet Inception Distance (FID), Diversity, and a few more. Furthermore, we continued evaluation using classification metrics such as accuracy, precision, recall, and a few others. Joint-related features or kinematic parameters were extracted, and the system assessed model performance against unseen data. Our findings demonstrate that the NGN algorithm produces more realistic and emotionally distinct body motion data and does so with more synthesizing speed than existing methods.

This paper reports on performance assessment of an algorithm developed to align functional Magnetic Resonance Image (fMRI) time series. The algorithm is based on the assumption that the human brain is subject to rigid-body motion and has been devised by pipelining fiducial markers and tensor based registration methodologies. Feature extraction is performed on each fMRI volume to determine tensors of

Modeling and vibration of a flexible link manipulator with tow flexible links and rigid joints are investigated which can include an arbitrary number of flexible links. Hamilton principle and finite element approach is proposed to model the dynamics of flexible manipulators. The links are assumed to be deflection due to bending. The association between elastic displacements of links is investigated, took into account the coupling effects of elastic motion and rigid motion. Flexible links are treated as Euler-Bernoulli beams and the shear deformation is thus abandoned. The dynamic behavior due to flexibility of links is well demonstrated through numerical simulation. The rigid-body motion and elastic deformations are separated by linearizing the equations of motion around the rigid body reference path. Simulation results are shown on for both position and force trajectory tracking tasks in the presence of varying parameters and unknown dynamics remarkably well. The proposed method ca...

ÓÐÀÂÍÅÍÈß ÑÌÅØÀÍÍÎÃÎ ÒÈÏÀ ÂÒÎÐÎÃÎ ÐÎÄÀ Ñ ÓÑËÎÂÈßÌÈ Àííîòàöèÿ.  äàííîé ðàáîòå, èñïîëüçóÿ ñâîéñòâà îáîáùåííûõ ðåøåíèé, êàê â ãèïåðáîëè÷åñêîé ÷àñòè, òàê è â ýëëèïòè÷åñêîé ÷àñòè ñìåøàííîé îáëàñòè, èññëåäóåòñÿ êðàåâàÿ çàäà÷à ñ êîíîðìàëüíîé ïðîèçâîäíîé äëÿ óðàâíåíèÿ ñìåøàííîãî òèïà âòîðîãî ðîäà ñ óñëîâèÿìè òèïà Ôðàíêëÿ. Åäèíñòâåííîñòü ðåøåíèÿ èññëåäóåìîé çàäà÷è äîêàçûâàåòñÿ ñ ïîìîùüþ ïðèíöèïà ýêñòðåìóìà, ïðè äîêàçàòåëüñòâå ñóùåñòâîâàíèÿ ðåøåíèÿ çàäà÷è ïðèìåíÿþòñÿ òåîðèè ñèíãóëÿðíûõ èíòåãðàëüíûõ óðàâíåíèé, èíòåãðàëüíûõ óðàâíåíèé ÂèíåðàÕîïôà è Ôðåäãîëüìà âòîðîãî ðîäà. Êëþ÷åâûå ñëîâà: óðàâíåíèå âòîðîãî ðîäà, ïðèíöèï ýêñòðåìóìà, óðàâíåíèå ÂèíåðàÕîïôà, óðàâíåíèå òèïà ñâåðòêè, ôóíêöèÿ Ãðèíà, åäèíñòâåííîñòü è ñóùåñòâîâàíèå ðåøåíèÿ.

Дан критический анализ теории черных дыр, в рамках которого рас-
сматривается более общий вопрос о том, являются ли все следствия какого-либо аналитического решения уравнения Эйнштейна неоспоримыми исти-нами с точки зрения общей теории относительности. Рассмотрена геометрия «внутренней» области пространства-времени Тауба-НУТ и показано, что ее геометрические свойства находятся в противоречии с фундаментальными положениями этой теории. Утверждается, что в этом случае
математический факт, каким является решение Тауба-НУТ, не может считаться своего рода абсолютной истиной, которую физики обязаны принять в целом, и что отношение к нему может определяться только здравым смыслом и обращением к физическому мышлению. Это приводит к выводу, что черные дыры не существуют.

This article deals with the kinematics of serial manipulators. The serial manipulators are assumed to be rigid and are modeled using the well-known Denavit-Hartenberg parameters. Two well-known problems in serial manipulator kinematics, namely the direct and inverse problems, are discussed and several examples are presented. The important concept of the workspace of a serial manipulator and the approaches to determine the workspace are also discussed.

Аннотация Рассмотрен вопрос о возможности нарушения пространственной четности как свойства пространства-времени. Показано, что это нарушение достигается нетривиальным объединением алгебр Ли временных сдвигов и пространственных вращений. Геометрия стационарного сферически симметричного пространства-времени построена в общем виде. Нарушение пространственной четности в пространстве-времени построенного таким образом, продемонстрировано на свойствах геодезических потоков, а именно, показано, что зеркальное отражение такого потока не является геодезическим потоком. Построение, представленное в настоящей работе, показывает путь, на котором, по нашему мнению, была построена метрика Тауба-НУТ.

Термин «вращение» используется для обозначения различных явлений и его смысл выбирается в зависимости от контекста, заданного областью науки, в которой он применен в данном конкретном случае. Показано, что во всем разнообразии своих проявлений вращение может быть как локальным, так и глобальным. Локальные вращения могут формировать неголономные поля локальных систем отсчета и в этом качестве они интересны с точки зрения понятия гравимагнитного заряда. Показана также взаимосвязь между такими полями и понятием векторного потенциала как выражением такого неголономного поля локальных вращающихся систем. В качестве источников векторного и ко-векторного потенциалов рассмотрены вращающиеся электрический заряд масса, а также гипотетические магнитный и гравимагнитный заряды, называемые также монополями. Решение одной из задач движения частиц в них, а именно – поле магнитного
монополя, полученное в XIX в., приведено, из трех остальных решаются только три, их решения приведены.

This paper tackles the problem of computing smooth, optimal trajectories on the Euclidean group of motions SE(3). The problem is formulated as an optimal control problem where the cost function to be minimized is equal to the integral of the classical curvature squared. This problem is analogous to the elastic problem from differential geometry and thus the resulting rigid body motions will trace elastic curves. An application of the Maximum Principle to this optimal control problem shifts the emphasis to the language of symplectic geometry and to the associated Hamiltonian formalism. This results in a system of first order differential equations that yield coordinate free necessary conditions for optimality for these curves. From these necessary conditions we identify an integrable case and these particular set of curves are solved analytically. These analytic solutions provide interpolating curves between an initial given position and orientation and a desired position and orientation that would be useful in motion planning for systems such as robotic manipulators and autonomous oriented vehicles.

Présenté par Philippe G. Ciarlet Nous établissons une version du lemme du déplacement rigide infinitésimal en coordonnées curvilignes lipschitziennes et en donnons une application aux modèles de coques linéairement élastiques dont la surface moyenne est lipschitzienne et le vecteur normal est également lipschitzien.

Présenté par Philippe G. Ciarlet Nous établissons une version du lemme du déplacement rigide infinitésimal en coordonnées curvilignes lipschitziennes et en donnons une application aux modèles de coques linéairement élastiques dont la surface moyenne est lipschitzienne et le vecteur normal est également lipschitzien.

Computing joint commands in real time by solving an inverse kinematic (IK) problem is an important manipulation task that is commonly encountered in agricultural operations such as fruit harvesting, disease detection and leaf sampling. To date, different numerical and analytical approaches have been proposed, and many of them are able to take constraints into account. In this study, a set of analytical algorithms is investigated to quickly solve the constrained five-degree-of-freedom inverse kinematic problem. The constraints due to actuator limitations and mechanical design of the mechanism are utilised in generating the solution sets for joint variables. Also a suboptimal solution for the inverse kinematic problem within this set is derived. The proposed methods are compared with a typical numerical solution based on non-linear constrained optimisation. It is shown that the proposed analytical and suboptimal semi-analytical solutions can be found in a much quicker fashion as compared to the non-linear constrained optimisation approach. The algorithms are validated by the handling mechanism in a ground robot platform specifically designed to operate in strawberry orchards.

The capability of using a linear kinetic energy harvester -A cantilever structured piezoelectric energy harvesterto harvest human motions in the real-life activities is investigated. The whole loop of the design, simulation, fabrication and test of the energy harvester is presented. With the smart wristband/watch sized energy harvester, a root mean square of the output power of 50 μW is obtained from the real-life hand-arm motion in human's daily life. Such a power is enough to make some low power consumption sensors to be self-powered. This paper provides a good and reliable comparison to those with nonlinear structures. It also helps the designers to consider whether to choose a nonlinear structure or not in a particular energy harvester based on different application scenarios.

A high fidelity model is developed for an elastic string pendulum, one end of which is attached to a rigid body while the other end is attached to an inertially fixed reel mechanism which allows the unstretched length of the string to be dynamically varied. The string is assumed to have distributed mass and elasticity that permits axial deformations. The rigid body is attached to the string at an arbitrary point, and the resulting string pendulum system exhibits nontrivial coupling between the elastic wave propagation in the string and the rigid body dynamics. Variational methods are used to develop coupled ordinary and partial differential equations of motion. Computational methods, referred to as Lie group variational integrators, are then developed, based on a finite element approximation and the use of variational methods in a discrete-time setting to obtain discrete-time equations T. Lee ( )

We discuss the bihamiltonian geometry of the Toda lattice (periodic and open). Using some recent results on the separation of variables for bihamiltonian manifold, we show that these systems can be explicitly integrated via the classical Hamilton-Jacobi method in the so-called Darboux-Nijenhuis coordinates.

This study applies variational integrators to the three-body problem, a classic problem from celestial mechanics that asks for the motion of three masses in space under mutual gravitational interaction. The use of variational integrators, a class of numerical methods used to simulate mechanical systems, is of value because they are known to exhibit accurate behavior with respect to the preservation of physical constants of motion when applied to systems with conserved quantities like energy and momentum. This contrasts with the performance of other numerical differential equation-solving algorithms like the RungeKutta method, which typically experience artificial dissipation of conserved quantities over successive iterations. A comparison of the performance of variational integrators versus the fourth-order RungeKutta method applied to the planar circular restricted three-body problem composes the core of this study. In particular, the algorithms are evaluated based on their ability...