Inertia Of Body Research Articles

The rotational inertia of a rigid body

The role of moment for inertia in rotational dynamics is equivalent to mass in linear dynamics and can be understood as an object's resistance to rotational motion. It establishes the relationship between several quantities such as angular momentum, angular velocity, torque, and angular acceleration. Accurately calculating the moment of inertia is crucial for designing various rotating systems and mechanical devices in engineering. For example, when dealing with rotating mechanical parts or machines, their moment of inertia ensures stability and performance in design needs to be considered. In physics and engineering, the analysis of rotational motion for rigid bodies relies on the concept of moment of inertia. It allows us to understand the dynamic behavior of a rigid body around an axis, including applications such as rotational stability, gyroscopic motion, and conservation of angular momentum. In this paper, the rotational inertia of a rigid body is studied by different method. Calculating the moment of inertia helps us gain a deeper understanding of an object's inertial properties during rotational motion while providing an important foundation for engineering design, scientific research, and material analysis.

Using your head - cranial steering in pterosaurs.

The vast majority of pterosaurs are characterized by relatively large, elongate heads that are often adorned with large, elaborate crests. Projecting out in front of the body, these large heads and any crests must have had an aerodynamic effect. The working hypothesis of the present study is that these oversized heads were used to control the left-right motions of the body during flight. Using digital models of eight non-pterodactyloids ("rhamphorhyncoids") and ten pterodactyloids, the turning moments associated with the head + neck show a close and consistent correspondence with the rotational inertia of the whole body about a vertical axis in both groups, supporting the idea of a functional relationship. Turning moments come from calculating the lateral area of the head (plus any crests) and determining the associated lift (aerodynamic force) as a function of flight speed, with flight speeds being based on body mass. Rotational inertias were calculated from the three-dimensional mass distribution of the axial body, the limbs, and the flight membranes. The close correlation between turning moment and rotational inertia was used to revise the life restorations of two pterosaurs and to infer relatively lower flight speeds in another two.

Influence of vibratory conveyor design parameters on the trough motion and the self-synchronization of inertial vibrators

Abstract A spatial model of a vibratory conveyor supported on steel-elastomer vibration isolators and vibrated by two inertial vibrators is presented in this article. The results of analyses of the effect of the layout of vibrators on the operation of the conveyor are presented. Displacement of the line of action of vibrators resultant force beyond the machine mass center causes the drift of the trough movement from the desirable rectilinear motion and problems associated with the unevenness of material movement. Three main cases were analyzed in the article: the displacement of the center of mass of the machine body from the straight line of action of the resultant for the vibrators, rotation of the main axes of inertia of the conveyor body in the working plane of the conveyor, and the oblique-angular resonance. The model presented in this article is used to consider coupling between vibrators and the body of the machine, which is responsible for the process of self-synchronization of the vibrators and the correctness of machine operation. The results of the theoretical analyses presented in this article were verified by laboratory tests and references to observations based on the authors’ industrial experience.

An orientation-adaptive electromagnetic energy harvester scavenging for wind-induced vibration

Wind energy is widely distributed, pollution-free and sustainable. Harvesting wind-induced vibration energy is a promising way to build self-powered systems. However, most of the current wind-induced vibration energy harvesters are unidirectional directional and insensitive to the frequently changing in wind direction. To overcome the difficulty, this work proposes an orientation-adaptive electromagnetic energy harvester (EMEH). By introducing a rotatable bluff body, the EMEH could be self-regulated to cater for the wind flow direction. Experimental results showed that the output power of the proposed EMEH could be enhanced greatly with the increase of rotatory inertia of the rotating bluff body. And, when the stiffness of the elastic beam is high, the output performance of the EMEH can be guaranteed by increasing the rotatory inertia of the rotatable bluff body. The output power of the optimized rotating bluff body and the elastic beam is 0.498 mW and 0.673 mW at wind speeds of 5.22 m/s and 8.0 m/s, respectively.

Phase shift between joint rotation and actuation reflects dominant forces and predicts muscle activation patterns.

During behavior, the work done by actuators on the body can be resisted by the body's inertia, elastic forces, gravity, or viscosity. The dominant forces that resist actuation have major consequences on the control of that behavior. In the literature, features and actuation of locomotion, for example, have been successfully predicted by nondimensional numbers (e.g. Froude number and Reynolds number) that generally express the ratio between two of these forces (gravitational, inertial, elastic, and viscous). However, animals of different sizes or motions at different speeds may not share the same dominant forces within a behavior, making ratios of just two of these forces less useful. Thus, for a broad comparison of behavior across many orders of magnitude of limb length and cycle period, a dimensionless number that includes gravitational, inertial, elastic, and viscous forces is needed. This study proposes a nondimensional number that relates these four forces: the phase shift (ϕ) between the displacement of the limb and the actuator force that moves it. Using allometric scaling laws, ϕ for terrestrial walking is expressed as a function of the limb length and the cycle period at which the limb steps. Scale-dependent values of ϕ are used to explain and predict the electromyographic (EMG) patterns employed by different animals as they walk.

Control of the Rotation of a Solid (Spacecraft) with a Combined Optimality Criterion Based on Quaternions

The dynamic problem of the optimal rotation of a rigid body (for example, a spacecraft) from an arbitrary initial to a designated final angular position in the presence of restrictions on the control variables is studied. Rotation time is not fixed. To optimize the rotation control program, a combined quality criterion is used, the minimized functional combines the energy costs and the duration of the maneuver in a given proportion. Based on the L. S. Pontryagin maximum principle and quaternion models of controlled motion of a solid, a solution to the problem was obtained. The reorientation optimality conditions are written in analytical form, and the properties of optimal rotation are shown. To construct an optimal rotation program, formalized equations and calculation formulas are written. Optimal control is presented in the form of a synthesis. The control law is formulated as an explicit dependence of the control variables on the phase coordinates. Analytical equations and relations for finding the optimal motion are given. Key relationships are given that determine the optimal values of the parameters of the rotation control algorithm. A constructive scheme for solving the boundary value problem of the maximum principle for arbitrary rotation conditions (initial and final positions and moments of inertia of a rigid body) is also described. For a dynamically symmetric rigid body, a closed-form solution of the reorientation problem is obtained. A numerical example and the results of mathematical modeling are presented, demonstrating the practical feasibility of the developed method for controlling the attitude of a spacecraft.

Design and analysis of a cable-driven gravity compensation mechanism for spatial multi-DoF robotic systems

The gravity compensation mechanisms (GCMs) are widely used in robotic manipulators and exoskeletons. This paper presents a cable-driven GCM applied in a spatial multi-degree-of-freedom (DoF) robotic system. By combining the cable transmission with the spring-based GCM, the whole compensation system is placed outside the main body of the robotic system, including the movable links and revolute joints. Therefore, the complexity and inertia of the robotic system's main body are reduced, and the motion range will not be limited by the mechanism for compensation, such as parallelogram linkages. Here presents the application example of a cable-driven four-DoF exoskeleton to demonstrate the development of the proposed GCM. The GCM is analyzed based on the space mapping method, and the mechanical models are designed based on theoretical analysis to evaluate the technical feasibility. The effectiveness of the proposed GCM is validated by calculating and analyzing the cable tension required by the exoskeleton and generated by the GCM in several specific movements. Finally, some limitations and potential applications of this cable-driven GCM are discussed.

Research on the Measurement Technology of Rotational Inertia of Rigid Body Based on the Principles of Monocular Vision and Torsion Pendulum

Damping is an important factor contributing to errors in the measurement of rotational inertia using the torsion pendulum method. Identifying the system damping allows for minimizing the measurement errors of rotational inertia, and accurate continuous sampling of torsional vibration angular displacement is the key to realizing system damping identification. To address this issue, this paper proposes a novel method for measuring the rotational inertia of rigid bodies based on monocular vision and the torsion pendulum method. In this study, a mathematical model of torsional oscillation under a linear damping condition is established, and an analytical relationship between the damping coefficient, torsional period, and measured rotational inertia is obtained. A high-speed industrial camera is used to continuously photograph the markers on a torsion vibration motion test bench. After several data processing steps, including image preprocessing, edge detection, and feature extraction, with the aid of a geometric model of the imaging system, the angular displacement of each frame of the image corresponding to the torsion vibration motion is calculated. From the characteristic points on the angular displacement curve, the period and amplitude modulation parameters of the torsion vibration motion can be obtained, and finally the rotational inertia of the load can be derived. The experimental results demonstrate that the proposed method and system described in this paper can achieve accurate measurements of the rotational inertia of objects. Within the range of 0–100 × 10−3 kg·m2, the standard deviation of the measurements is better than 0.90 × 10−4 kg·m2, and the absolute value of the measurement error is less than 2.00 × 10−4 kg·m2. Compared to conventional torsion pendulum methods, the proposed method effectively identifies damping using machine vision, thereby significantly reducing measurement errors caused by damping. The system has a simple structure, low cost, and promising prospects for practical applications.

Evaluation of CMIP6 models for simulations of diurnal temperature range over Africa

The variability in the diurnal temperature range (DTR), an indicator of climate change, remains limited, especially over Africa, due to the scarcity of observed maximum and minimum temperature data. This work investigates the ability of the Coupled Model Intercomparison Project (CMIP6) to simulate DTR over Africa for the period 1980–2014. Datasets from the Climatic Research Unit (CRU TS4.05) and National Oceanic and Atmospheric Administration (NOAA) Climate Prediction Centre (CPC) gridded temperature datasets are utilized as observed data. Similar to the high variability in topography and climate across the continent, the DTR exhibits high heterogeneity over Africa. The Sahara and its environs record the highest DTR, while Central Africa and coastal areas experience the least, given the thermal inertia of water bodies. CMIP6 models overestimate and underestimate DTR over different parts of the continent. Moreover, the multi-model ensemble mean of CMIP6 models shows significant decreasing trends both in seasonal and annual trends. Overall, five CMIP6 models such as EC-Earth3, ACCESS-CM2, BCC-CSM2-MR, EC-Earth3-veg, and IPSL-CM6A-LR show robust skill scores (0.48–0.54). The findings form the basis for investigating the role of temperature extremes on DTR. Further, the variability in DTR across parts of the continent prompts the need for future assessments to investigate future changes in DTR.

Methodological features of using of the element «squat»

The paper analyzes the technical element «squat», considers the options for its use in choreography and their interpretation in national associations, highlights the basic parts of this movement, typical for different squats. A general scheme of the «squat» element is proposed, which allows one to freely master and apply it, depending on the increase in the level of theoretical material and practical implementation, thus avoiding significant indicators that should be combined with technical development and a variety of assortment of this element of martial arts. Examples of the use of a squat in the form of a counterattack are given, using the energy of the body's inertia in the process of transition from a standing position to a crouching position. The effectiveness of plyometric exercises in the conditions of modern training and the possibility of their wide use in the form of such an element as a «squat» are considered. The expediency of using this element as a means of developing speed-strength abilities is also substantiated. Various classic and innovative options for using squats are presented, both in a practical and applied aspect, and in the aspect of effective development of physical qualities. Proposes the author's method of using the squat as an element of an applied nature, and as a means of developing speed-strength qualities.

Influence of dissipative asymmetry on the of rotation stability in a resisting medium of a asymmetric rigid body under the action of a constant moment in inertial reference frame

Assuming that the center of mass of an asymmetric rigid body is located on the third main axis of inertia of a rigid body, the influence of dissipative asymmetry on the stability of uniform rotation in a medium with resistance of a dynamically asymmetric rigid body is estimated. A rigid body rotates around a fixed point, is under the action of gravity, dissipative moment and constant moment in an inertial frame of reference. The stability conditions are represented by a system of three inequalities. The first and second inequalities have the first degree with respect to the dissipative asymmetry, and the third inequality has the third degree. The third inequality is the most difficult to study. Analytical studies of the influence of small and large dissipative asymmetries, restoring, overturning and constant moments on the stability of rotation of a rigid body are carried out. Conditions for asymptotic stability are obtained for sufficiently small values of the dissipative asymmetry and conditions for instability for sufficiently large values of the asymmetry. The stability conditions are written down to the second order of smallness with respect to the constant moment and the first - with respect to the restoring or overturning moments. Stability conditions for the rotation of a rigid body around the center of mass are studied.

Growth constraints set an upper limit to theropod dinosaur body size

Despite nearly 200years of scientific collecting and study, none of the extinct, bipedal, predatory, theropod dinosaurs have been reliably shown to exceed 12m in length. Using digital 3D models of theropods with lengths spanning 80cm to 12m, their body masses were found to scale to the 3.5 power of body lengths. The lateral area of the pelvis and the cross-sectional area of the tail base of these animals corresponds to the cross-sectional areas of key muscle groups important for balance and locomotion, and both scale to the 2.4 power of body length. Body accelerations in the lateral and forward directions are, using F = ma, given by dividing muscle area (force proxy) by body mass. Plotting these acceleration estimates against body length shows them to decrease exponentially. The largest theropods with body lengths of 10-12m have less than 10% of the acceleration capacity of the smaller forms. The distinct lack of fossil remains of theropods demonstrably longer than 12m suggests that the theropod body plan had an upper size limit based on a minimum acceleration threshold. Rotational inertia of the theropod body was found to be proportional to body length raised to the 5.5 power, and with increasing length, the capacity for agility would rapidly diminish. The tight relationship between theropod pelvic area and body length allows for the estimation of body lengths of specimens lacking complete axial skeletons, and this is done for four, large, well-preserved pelves.

Об эффекте Зоммерфельда и скрытых колебаниях в асинхронном электроприводе горных машин

Рассмотрена возможность возникновения эффекта Зоммерфельда и скрытых колебаний в электромеханических системах самоходных горных машин. Отмечено, что по результату воздействия на механическое передаточное устройство (редуктор) режим пуска асинхронного электродвигателя (АД) прямым включением в сеть эквивалентен работе двигателя в опыте Зоммерфельда с эксцентрично расположенным грузиком при воздействии его на фундамент двигателя. При этом изменения положения корпуса статора АД могут повлечь за собой периодические изменения абсолютной скорости вращения электромагнитного поля статора, что приведет к возникновению во всей электромеханической системе электропривода колебаний, классифицируемых как скрытые (hidden oscillations). В качестве примера рассмотрен режим пуска проходческого комбайна КСП-32. Пример показал, что значения момента инерции корпуса комбайна могут изменяться в зависимости от загрузки углем питателя и скребкового конвейера, это означает необходимость выполнения вариантов численного моделирования для различных моментов инерции. Приведены результаты расчетов. Сделан вывод, что в электромеханических системах самоходных горных машин практически всегда при пусках можно наблюдать проявление эффекта Зоммерфельда и возникновение низкочастотных скрытых колебаний. Теоретическое предсказание этих явлений затруднено и может быть обнаружено путем численного моделирования вариантов режимов работы цифрового двойника горной машины.

ВПЛИВ ДИНАМІЧНОЇ НЕСИМЕТРІЇ НА СТІЙКІСТЬ ОБЕРТАННЯ У СЕРЕДОВИЩІ З ОПОРОМ ТВЕРДОГО ТІЛА ПІД ДІЄЮ ПОСТІЙНОГО МОМЕНТУ У ІНЕРЦІАЛЬНІЙ СИСТЕМІ ВІДЛІКУ

Under the assumption that the center of mass of an asymmetric rigid body is located on the third principal axis of inertia of a rigid body, the previously obtained conditions for the asymptotic stability of uniform rotation in a medium with resistance of a dynamically asymmetric rigid body are investigated. A rigid body rotates around a fixed point, is under the action of gravity, dissipative moment and constant moment in an inertial frame of reference. The stability conditions are presented as a system of three inequalities. The first and second inequalities have the first degree relative to the dynamic unbalance, and the third inequality has the third degree. The first and third inequalities are of the second degree with respect to the overturning or restoring moment, and the second inequality is of the first degree. The first and third inequalities are of the fourth degree with respect to the constant moment, and the second inequality is of the second degree. The third inequality is the most difficult to study. Analytical studies of the influence of dynamic unbalance, restoring and overturning moments on the conditions of asymptotic stability are carried out. Conditions for the asymptotic stability of uniform rotation in a medium with resistance to an asymmetric rigid body are obtained for sufficiently small values of dynamic unbalance. Sufficient stability conditions are written out up to the second order of smallness with respect to the constant moment and the first order of smallness with respect to the restoring and overturning moments. Instability conditions are obtained for sufficiently large dynamic unbalance. The effect of dynamic unbalance on the stability conditions for the rotation of a rigid body around the center of mass is studied. It is shown that in the absence of dissipative asymmetry, it is sufficient for asymptotic stability that the axial moment of inertia of a rigid body be greater than the double equatorial moment and that the well-known necessary stability condition for a symmetric rigid body be satisfied.

Efficient sliding locomotion of three-link bodies with inertia

Many previous studies of sliding locomotion have assumed that body inertia is negligible. Here we optimize the kinematics of a three-link body for efficient locomotion and include among the kinematic parameters the temporal period of locomotion, or equivalently, the body inertia. The optimal inertia is nonnegligible when the coefficient of friction for sliding transverse to the body axis is small. Inertia is also significant in a few cases with relatively large coefficients of friction for transverse and backward sliding, and here the optimal motions are less sensitive to the inertia parameter. The optimal motions seem to converge as the number of frequencies used is increased from one to four. For some of the optimal motions with significant inertia we find dramatic reductions in efficiency when the inertia parameter is decreased to zero. For the motions that are optimal with zero inertia, the efficiency decreases more gradually when we raise the inertia to moderate and large values.

Efficient bending and lifting patterns in snake locomotion

We optimize three-dimensional snake kinematics for locomotor efficiency. We assume a general space-curve representation of the snake backbone with small-to-moderate lifting off the ground and negligible body inertia. The cost of locomotion includes work against friction and internal viscous dissipation. When restricted to planar kinematics, our population-based optimization method finds the same types of optima as a previous Newton-based method. With lifting, a few types of optimal motions prevail. We have an s-shaped body with alternating lifting of the middle and ends at small-to-moderate transverse friction. With large transverse friction, curling and sliding motions are typical at small viscous dissipation, replaced by large-amplitude bending at large viscous dissipation. With small viscous dissipation, we find local optima that resemble sidewinding motions across friction coefficient space. They are always suboptimal to alternating lifting motions, with average input power 10–100% higher.

Flexural Wave Propagation in Rigid Elastic Combined Metabeam

Abstract In this paper, flexural wave propagation, attenuation, and reflection through finite number of rigid elastic combined metabeam (RECM) elements sandwiched between two Euler Bernoulli beams has been studied, implementing the spectral element, inverse Fourier transform, and transfer matrix method. Spectral element has been formulated for the unit representative cell of RECM employing the rigid body dynamics. Governing dimensionless parameters are identified. Furthermore, the sensitivity analysis has been carried out to comprehend the influence of non-dimensional parameters, such as mass ratio, length ratio, and rotary inertia ratio on the attenuation profile. Rotary inertia of rigid body produces local resonance (LR) band, which may abridge the gap between the two Bragg scattering (BS) bands and results in an ultra-wide stop band for the specific combination of governing non-dimensional parameters. A total of 164% normalized attenuation band is possible to obtain in RECM. Natural frequencies for the finite RECM have also been evaluated from the global spectral element matrix and observed that some natural frequencies lie in the attenuation band. Therefore, the level of attenuation near that natural frequencies is significantly less and cannot be identified from the dispersion diagram of the infinite RECM.

Thermal regime, together with lateral connectivity, control aquatic invertebrate composition in river floodplains

Abstract Large river floodplains are dynamic environments, where alternating low and high flows are key ecological processes shaping aquatic biota. As a result of fluctuations in flow in floodplain channels, the diversity of benthic assemblages is assumed to result from the balance between surface flow connections, which are dominant during high flows, and groundwater inputs, which are dominant during low flows. However, the relative importance of these inputs in explaining aquatic invertebrate diversity has never been tested. The response of aquatic invertebrates to hydrological changes of a river floodplain was investigated in seven braided and six braided–anastomosed floodplain channels of the French upper Rhône River that are fed by three different processes: groundwater supply (which controls the thermal inertia of the water bodies), surface slow flow connections (i.e. diffuse overbank flows; passive overflow), and surface shear stress‐related connections (i.e. condensed flows; active overflow) during high flows. Generalised dissimilarity models indicated that floodplain invertebrate composition had complex relationships with the three processes considered. The relative importance of the latter appeared dependent upon the morphology of the floodplain channels. In the braided channels, the effects of shear stress‐related connections were more prominent than in the anastomosed ones, for which the effects of the three processes were more similar. Overall, the diversity of flow connections, that is, lateral surface water connections (both shear stress‐related and slow, as defined above) and vertical connection with groundwater (inferred through thermal inertia) enhanced the species turnover at the reach scale. Thermal inertia influenced invertebrate composition when, during low flow periods, surface flow connections had limited effect. Our results highlighted that the role of hydrologic connectivity upon floodplain diversity cannot be reduced to a single process. They also indicate the importance of vertical connectivity for maintaining biodiversity in floodplain habitats where surface flow connectivity is neither frequent nor constant.

Research of the market and economic state of enterprises in the cosmetics industry in the context of reforming the regulatory framework and harmonization in accordance with the requirements of the EU regulations

There is a certain dissonance between the rate of increase in demand, for an expanded range of perfumery and cosmetic goods, and the slow development of regulatory and legal regulation of their production and safety. During the research, it was established that the inertia of state bodies regarding the approval of laws has a significant impact on the economic development of industry enterprises. Problems in methods for determining substances have been identified; ambiguity of the legislative framework regarding the legal liability of producers for falsification, use of non-regulated components, labeling requirements. To solve the problem, a critical analysis of the regulatory impact of the regulatory framework, in time, on the economic condition and competitiveness of industry products was carried out. The legislative requirements put forward in Ukraine, EU countries, Canada, America, China on control of production and testing of cosmetics on animals have been analyzed. As a result of the research, four stages of reforming regulatory regulation by the state and bringing the legislative framework of the industry in line with European requirements have been identified and substantiated. New categories introduced into the regulatory framework have been identified and the prospects for exporting goods produced within the framework of the new regulatory framework are shown. Based on the results of the research, identical and different requirements of the Ukrainian and European regulations for cosmetic products, for packaging, labeling, methods for studying stability, physical and chemical indicators, sampling procedure for expert evaluation were established. It is shown that the introduced changes meet the requirements of European standards and could increase the competitiveness and investment potential of domestic enterprises of the cosmetic industry

ПРО СТІЙКІСТЬ РІВНОМІРНОГО ОБЕРТАННЯ У СЕРЕДОВИЩІ З ОПОРОМ НЕСИМЕТРИЧНОГО ТВЕРДОГО ТІЛА ПІД ДІЄЮ ПОСТІЙНОГО МОМЕНТУ У ІНЕРЦІАЛЬНІЙ СИСТЕМІ ВІДЛІКУ

Assuming that the center of mass of a rigid asymmetric body is on the third main axis of inertia of a rigid body, the conditions for the asymptotic stability of uniform rotation of a dynamically asymmetric solid rigid body with a fixed point are obtained. These conditions are obtained in the form of a system of three inequalities based on the Lénard-Shipar test, written in innormal form. The rigid body is under the action of gravity, dissipative moment and constant moment in the inertial frame of reference. The rotation of a rigid asymmetric body around the center of mass is studied. Uniform rotation around the center of mass of a rigid asymmetric body will be unstable in the absence of a constant moment. Cases of absence of dynamic or dissipative asymmetry are considered. It is shown that the equilibrium position of a rigid body will be stable only under the action of the reducing moment. Dynamic asymmetry has a more significant effect on the stability of rotation of an asymmetric rigid body than dissipative asymmetry. Stability conditions have been studied for various limiting cases of small or large values of restoring, overturning, or constant moments. It is noted that for sufficiently large values of the modulus of the reducing moment, the rotation of the asymmetric solid will be asymptomatically stable. If the axial moment of inertia is the greatest or the smallest moment of inertia, then at sufficiently large values of angular velocity, both under the action of the overturning moment and under the action of the reducing moment, the rotation of the asymmetric solid will be asymptomatically stable. Analytical studies of the influence of dissipative, constant, overturning and restorative moments on the stability of uniform rotations of asymmetric and symmetric solids have been carried out. It is shown that in the absence of dynamic and dissipative symmetries, the obtained stability conditions coincide with the known ones.