Teaching kinematic rotations is a daunting task for even some of the most advanced mathematical minds. However, envisioning and explaining the three-dimensional rotations can be highly simplified by changing the paradigm. This paradigm change allows for a high school student with a understanding of geometry to be able to not only develop the matrix but also explain the rotations at a collegiate level. The proposed method includes the assumption of a point (P) within the initial three-dimensional frame with axes (x ̂_i, y ̂_i, z ̂_i). It then utilizes a two-dimensional rotation view (2DRV) to measure how the coordinates of point P translate after the initial axis is rotated instead of using the established Euler's formula. The equations are used in matrix notation to develop a direction cosine matrix (DCM) for future equations. This method provides a high school student with an elementary and repeatable process to compose and explain kinematic rotations.

The signal-to-noise ratio (SNR) data is part of the global navigation satellite systems (GNSS) observables. In a marine environment, the oscillation of the SNR data can be used to derive reflector heights. Since the attenuation of the SNR oscillation is related to the roughness of the sea surface, the significant wave height (SWH) of the water surface can be calculated from the analysis of the attenuation. The attenuation depends additionally on the relation between the coherent and the incoherent part of the scattered power. The latter is a function of the correlation length of the surface waves. Because the correlation length changes with respect to the direction of the line of sight relative to the wave direction, the attenuation must show an anisotropic characteristic. In this work, we present a method to derive the wave direction from the anisotropy of the attenuation of the SNR data. The method is investigated based on simulated data as well by the analysis of experimental data from a GNSS station in the North Sea.

Natural fibers are being increasingly used in different areas of engineering, including as composite reinforcement. Among these fibers, carauá stands out for its good mechanical properties and adherence to resin. Nevertheless, little is known about the behavior of this material in the manufacture of a composite or whether classic failure theory can be used in this case. In this context, the present study assesses the mechanical properties of two laminas made of unidirectional curauá fiber with volumetric fiber percentages of 30 % and 22 %, and compares the results with the values obtained for four failure criteria reported in the literature, using analysis of variance (ANOVA). To that end, tensile tests were conducted in the direction of the fiber and at other loading angles, in addition to iosipescu shear tests. The results show that the maximum stress criterion does not represent the failure behavior of these materials and that the best was the Hashin criterion.

Since the first generation of 7xxx superhard aluminum alloy was investigated in 1930, hitherto the fifth generation aluminum alloy materials with high comprehensive properties such as high static strength, high strength, heat resistance, high toughness, damage resistance, low density and low quenching sensitivity have been improved and developed. This paper reviews the progress of 7xxx aluminum alloy materials in composition, microstructure, properties, preparation methods, heat treatment strengthening and applications from 2014 to 2021. The effect of adding trace elements on microstructure and properties of 7xxx series alloy and the problems existing in aging precipitation characteristics and reinforcement mechanism are discussed. The future development direction of 7xxx superhard aluminum alloy is prospected by optimizing heat treatment technological, adding appropriate trace elements to alloy and controlling alloy microstructure.

This study investigated the effects of two plyometric training protocols on sprint and change of direction (COD) performance in elite hockey players. A parallel-group randomized controlled trial design was used and seventeen elite male and female field hockey players were randomly allocated into either low-to-high (L-H, n = 8) or high-to-low (H-L, n = 9) training groups. Each group performed separate variations of the drop jump exercise twice weekly for six weeks, with an emphasis on either jump height (L-H) or drop height (H-L). Performance variables assessed included sprint times over 10 m and 20 m, as well as 505 time. A two-way repeated measures analysis of variance was performed and Cohen’s d effect sizes were calculated. The H-L group displayed significant small ES improvement from baseline to post-training in the 10 m sprint (1.893 ± 0.08 s pre vs 1.851 ± 0.06 s post) (ES = −0.44) (P = <0.05). Small but not statistically significant differences between groups were observed for 10 m and 20 m sprint performance, and no significant differences were observed within or between groups for 505 time. These findings highlight the difficulty in substantially enhancing speed and COD ability in highly trained athletic populations through the addition of a low volume, short duration plyometric training protocol.

A method of direction-of-arrival (DoA) estimation for FMCW radars is presented. In addition to MUSIC and ESPRIT, which are well-known high-resolution DoA estimation algorithms, deep learning has recently emerged as a very promising alternative. It is proposed in this paper to use a 3D convolutional neural network (CNN) for DoA estimation. The 3D-CNN extracts from the radar data cube spectrum features of the region of interest (RoI) centered on the potential positions of the targets, thereby capturing the spectrum phase shift information, which corresponds to DoA, along the antenna axis. Finally, the results of simulations and field experiments are provided to demonstrate the superior performance, as well as the limitations, of the proposed 3D-CNN.

Background: Military pilots show high visuo-spatial skills. Previous studies demonstrate that they are better in mental rotating a target, in taking different perspectives, in estimating distances, in travel planning and in topographic memory. Here, we compared navigational cognitive styles between military pilots and people without flight experience. Pilots were expected to be more survey users than non-pilots, showing higher navigational strategies. Method: 106 jet military pilots of Italian Air Force and 92 non-pilots were enrolled in order to investigate group differences in navigational styles. Participants were asked to perform a reduced version of the Spatial Cognitive Style Test – SCST, consisting of six tasks that allow to distinguish individuals in landmark (people orient themselves by using a figurative memory for environmental objects), route (people use an egocentric representation of the space) and survey (people have a map-like representation of the space) users. Results: In line with our hypothesis, military pilots mainly adopt a survey style, whereas non-pilots mainly adopt the route style. In addition, pilots outperformed non pilots in both the 3D-Rotation task and Map Description Task. Conclusion: Military flight expertise influences some aspects of the spatial ability, leading to enhance human navigation. Although, it must be considered that they are a population whose navigational skills were already high at the time of selection at the academy before formal training began.

The accuracy of wind field simulation and prediction is one of the most significant parameters in the field of atmospheric science and wind energy. Limited by the observation data, there are few researches on wind energy development. A 3D Doppler wind lidar (DWL) providing the high-vertical-resolution wind data over the urban complex underlying surface in February 2018 was employed to evaluated the accuracy of vertical wind field simulation systematically for the first time. 11 PBL schemes of the Weather Research and Forecasting Model (WRF) were employed in simulation. The model results were evaluated in groups separated by weather (sunny days, haze days and windy days), observation height layers, and various observation wind speeds. The test results presented that the vertical layer altitude of the observation point position was the most important factor. The simulation is fairly well at a height of 1000-2000m, as most of the relative mean bias of wind speed and wind direction are less than 20% and 6% respectively. Below 1000 m, the wind speed and direction biases are about 30%-150% m.s-1 and 6%-30% respectively. Moreover, when the observed wind speed was lower than 5 m.s-1, the bias were usually large, and the wind speed relative mean bias is up to 50-300%. In addition, the accuracy of simulated wind profile is better in 10-15m.s-1 than other speed ranges, and is better up 1000m than below 1000m in the boundary layer. We see that the WRF boundary layer schemes have different applicability to different weather conditions. The WRF boundary layer schemes have significant differences in wind field simulation with larger error under the complex topography. A PBL scheme is not likely to maintain its advantages in the long term under different conditions including altitude and weather conditions.

The feasibility of a steady-state visual evoked potential (SSVEP) brain-computer interface (BCI) with a single flicker stimulus for multiple-target decoding has been demonstrated in a number of recent studies. The single-flicker BCIs have mainly employed the direction information for encoding the targets, i.e. different targets are placed at different spatial directions relative to the flicker stimulus. The present study explored whether visual eccentricity information can also be used to encode target for the purpose of increasing the number of targets in the single-flicker BCIs. A total number of 16 targets were encoded, placed at eight spatial directions, and two eccentricities (2.5° and 5°) relative to a 12 Hz flicker stimulus. Whereas distinct SSVEP topographies were elicited when participants gazed at targets of different directions, targets of different eccentricities were mainly represented by different signal-to-noise ratios (SNRs). Using a canonical correlation analysis-based classification algorithm, simultaneous decoding of both direction and eccentricity information was achieved, with an average offline 16-class accuracy of 66.8±16.4% averaged over 12 participants and a best individual accuracy of 90.0%. Our results demonstrate a single-flicker BCI with a substantially increased target number towards practical applications.

Cellular substructure has been widely observed in the sample fabricated by laser powder bed fusion, while its growth direction and the crystallographic orientation have seldom been studied. This research tries to build a general model to construct the substructure from its two-dimensional morphology. All the three Bunge Euler angles to specify a unique growth direction are determined, and the crystallographic orientation corresponding to the growth direction is also obtained. Based on the crystallographic orientation, the substructure in the single track of austenitic stainless steel 316L is distinguished between the cell-like dendrite and the cell. It is found that, with the increase of scanning velocity, the substructure transits from cell-like dendrite to cell. When the power is 200 W, the critical growth rate of the transition in the single track can be around 0.31 ms^-1.

In this paper, we considered two phenomena in acoustically excited aqueous solutions of a strong electrolyte. These are the well-known Debye ionic vibrational potential (IVP), and radiofrequency anisotropy we discovered earlier , apparently, for the first time. Since both occur due to the accelerated motion of the solution, we have tried to combine them in one simple model. We have established that for a polarized UHF radio wave passed through a NaCl aqueous solution excited by an acoustic pulse the rotation angle of its vector E is proportional to the integral of the square of the observing IVP over time. An equivalent electrical circuit simulating the observed phenomena has been proposed and tested for physical feasibility. Several arguments are given in favour of the fluid-gyroscopic mechanism of RF anisotropy-related effects. We also found out that the IVP is practically independent of the vibrational velocity for frequencies below 10 kHz and it tends to zero at zero frequency. The latter is consistent with the law of conservation of energy but contradicts the incomplete existing theory.

Enhancing the effectiveness of search and rescue operation at sea is always a duty of utmost importance of the coastal states. The search area for distressed objects can be determined by using Monte Carlo simulation, combined with the Median-Filter. Once the search area has been identified, the success of search and rescue operations depends on the sweeping ability of search and rescue vessel at the probability area of the distress object with the minimum time. This is the important element to the success of the search and rescue operation as it minimizes the risk and cost for Search and rescue team. In this article, the authors study and propose the use of Bacterial Foraging Optimization Algorithm (BFOA) to calculate the optimal search and co-ordination route for many search and rescue vessels in Vietnam sea. The simulation results show that it is quite consistent with reality and BFOA can be effectively applied to determine a quick search.

The calculation of the exact value of the square root of 2 is requested. In order to obtain its infinite value, A new concept is proposed where the accumulations of the infinitely many of finity is indicated by the change in direction which means that there is a jump from finity to infinity .The meaningless for an infinite number with a decimal point is indicated by this jump because any decimal number only have meanings within a finite range values and there is only an infinite integer quantity that can not be operated by algorithms like operations of multiplication，division,addition, and subtraction . The final result of the change in direction is two quantity where the second quantity and the first quantity extend in parallel line and never intersect and the second quantity represent the size of the first quantity. The first quantity is the infinitely great that can't be talked about anything outside of it and can compress any quantities outside of it to nothing and it is the exact value of the square root of 2 .

Aim of expressional space is to facilitate the public to explore their hobby and talent in autodidact. The space for expression in Makassar City is necessary for the mural artist and the youngsters who has a hobby to play a skateboard. Their talent is insufficient attention by the government and create negative attitude because there no space to accommodate their activity. Therefore, this paper presents a design idea of expressional space by implementing the architectural geometry. The architectural geometry design principle is based on simple geometry form application as a realization of form from the space. An experience of the space for the user realizes by the relationship between the space and the interaction with the environment through geometry and form processing as the basic of the creation process in the architectural works. Content analysis method providing a landscape layout and transformation of form and building mass in form of the implementation of architectural geometry principles. The principles are pure geometry, composition of geometry, direction wall, and opening for the transformation process of expressional space form to produce and increase aesthetic value of the environment.

Although the Slicing Method (SM) is effective for calculating the volume of point cloud objects (PCOs), it is restricted in terms of applicability and practicability because of a certain contingency and directional defects. The Co-Opposite-Direction Slicing Method (CODSM) proposed in this paper is an improved method for calculating PCO volume by increasing parallel (co-opposite-direction) observation and considering the two-way mean as the result. This method takes full advantage of the mutual offsetting of random errors and the compensation of systematic directional errors, which can effectively overcome (or mitigate) the effect of random errors and reduce the effect of systematic errors in SM. In this paper, two typical objects, a cone model and a stone lion base, are the examples for calculating PCO volume using CODSM. The results show that CODSM has all the inherent advantages of SM and effectively weakens the volatility of random errors and the directionality of systematic errors from SM. Therefore, CODSM is a robust configuration upgrade of SM.

The extended finite element method (XFEM) is now widely used in crack simulations and the direction of propagation of the XFEM crack in SS-304 has been quite interesting. This paper discusses the direction,θ(+ve in anti-clockwise direction), of the XFEM crack (under mode-I) propagation based on the von Mises stress-field around the crack-tip for static loading under the light water reactors (LWRs) conditions. The Mises core region from the crack-tip is chosen for β=〖90〗^o, the angle between the load and the initial crack. Experimental data for LWRs’environment is obtained and the simulations have been carried out applying three different static loads and results for the direction of the crack are calculated by measuring the stress-field around the crack-tip. It has been found that the direction of the XFEM varies inversely as the stress-field around the crack tip is increased. The computational results have been compared with the numerical results based on the minimum strain energy density criterion[S-criterion].

Let b∈Cn∖{0} be a fixed direction. We consider slice holomorphic functions of several complex variables in the unit ball, i.e. we study functions which are analytic in intersection of every slice {z0+tb:t∈C} with the unit ball Bn={z∈C:|z|:=|z|12+…+|zn|2&lt;1} for any z0∈Bn. For this class of functions there is introduced a concept of boundedness of L-index in the direction b where L:Bn→R+ is a positive continuous function such that L(z)&gt;β|b|1−|z|, where β&gt;1 is some constant. For functions from this class we describe local behavior of modulus of directional derivatives on every ’circle’ {z+tb:|t|=r/L(z)} with r∈(0;β],t∈C,z∈Cn. It is estimated by value of the function at center of the circle. Other propositions concern a connection between boundedness of L-index in the direction b of the slice holomorphic function F and boundedness of lz-index of the slice function gz(t)=F(z+tb) with lz(t)=L(z+tb). Also we show that every slice holomorphic and joint continuous function in the unit ball has bounded L-index in direction in any domain compactly embedded in the unit ball and for any continuous function L:Bn→R+.

A particular challenge in the conceptual design of direct-from orbit delivery systems is the seemingly well-known kinematics retain fallacies whose efficacies are reduced over great distances. Rotation about the local wing of an aerospace vehicle is almost never the pitch angle, yet modern application of kinematics often assumes such (with accompanying angular error). The same assertion is usually true about the nature of roll and yaw angles. Expressing motion in coordinates of rotating reference frames necessitates transformation between reference frames, and one such transformation is embodied in the Direction Cosine Matrices (DCM) formed by a sequence of three successive frame rotations. One of two ubiquitous sequences of three rotations used to construct the DCM involves first a rotation around the inertial z-axis, then intermediate y-axis, then finally about the body’s x-axis; a sequence commonly called the “aerospace sequence” or the a “3-2-1 rotation sequence”. The second ubiquitous sequence is the so-called “orbital sequence” or “3-1-3 rotation sequence” with rotations about the inertial z axis first, then about the intermediate x-axis, then finally about the body z-axis. This manuscript evaluates which sequence is the most advantageous for an object starting in space and then travels through the atmosphere to a target on the Earth’s surface. Six degrees of freedom of vehicle motion were simulated starting in orbit with a given thrust and commanded maneuver. The simulation performs all twelve possible rotation sequences (transforming inertial coordinates to body coordinates) with comparison by computational burden and error representing rotations about body axes (roll, pitch, and yaw respectively). Simulation precision is validated using the quaternion normalization condition indicating near machine precision (0.9\times{10}^{-15}) and reveals the so-called 132 rotation is the most accurate with an average error of 0.14° and a computational time of 0.013 seconds: resulting in a 97.95% increase in accuracy over the so-called 321 rotation and a 99.84% increase over the so-called 313 rotation.