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We consider collision of two particles in rotating spacetimes without horizons. If the metric coefficient responsible for rotation of spacetime is big enough, the energy of collisions in the center of mass frame can be as large as one likes. This can happen in the ergoregion only. The results are model-independent and apply both to relativistic stars and wormholes.

Unistable polyhedra are in equilibrium on only one of their faces. The smallest known homogeneous unistable polyhedron to date has 18 faces. Using a new optimization algorithm, we have found a unistable polyhedron with only 14 faces, which we believe to be a lower bound. Despite the simplicity of the formulation, computers were never successfully used for solving this problem due to the seemingly insurmountable dimensionality of the underlying mathematical apparatus. We introduce new optimization approaches designed to overcome the problem's intractability and discuss its significance to other application areas. We also mathematically prove the unistable property of the found bodies using rational arithmetic. Surprisingly enough, all of our computer-generated unistable polyhedra look similar to the human eye, providing important insights into the nature of the problem.

We give equations of motion for the center of mass and intrinsic angular momentum of axially symmetric sources that emit gravitational radiation. This symmetry is used to uniquely define the notion of total angular momentum. The center of mass then singles out the intrinsic angular momentum of the system.

If two particles collide inside the ergosphere, the energy in the center of mass frame can be made unbound provided at least one of particles has a large negative angular momentum [A. A. Grib and Yu. V. Pavlov, Europhys. Lett.101 (2013) 20004]. We show that the same condition can give rise to unbounded Killing energy of debris at infinity, i.e. super-Penrose process. Proximity of the point of collision to the black hole horizon is not required.

We consider stationary axially symmetric black holes with the background scalar field and test particles that can interact with this field directly. Then, particle collision near a black hole can lead to the unbounded energy $E_{\mathrm{\text{c}}.\mathrm{\text{m}}.}$ in the center of mass frame (contrary to some recent claims in literature). This happens always if one of the particles is neutral whereas another one has nonzero scalar charge. Kinematically, two cases occur here. (i) A neutral particle approaches the horizon with the speed of light while the velocity of the charged one remains separated from it (this is direct analogue of the situation with collision of geodesic particles.). (ii) Both particles approach the horizon with the speed almost equal to that of light but with different rates. As a result, in both cases the relative velocity also approaches the speed of light, so that $E_{\mathrm{\text{c}}.\mathrm{\text{m}}.}$ becomes unbounded. We consider also a case when the metric coefficient $g_{\varphi \varphi }\to 0$ near a black hole. Then, overlap between the geometric factor and the presence of the scalar field opens additional scenarios in which unbounded energy $E_{\mathrm{\text{c}}.\mathrm{\text{m}}.}$ is possible as well. We give a full list of possible scenarios of high-energy collisions for the situations considered.

We study the acceleration of charged particles by Reissner Nordström black hole by taking into account the term appearing in the formula of the center of mass energy due to charge of the particle. We consider that the particle is radially falling towards the black hole, i.e., $L=0$. It is found that the center of mass energy is infinitely large at the outer horizon without any constraint.

This paper considers the problem of the center of mass motion of three fermionic particles, e. g., equal nucleons (no spin), which can move only in the x-direction in the laboratory system. This system (with three degrees of freedom only) is transformed to a system where one coordinate is proportional to the center of mass coordinate. The center of mass moves in a harmonic oscillator potential. The basis set of wave functions is constructed with Hermite polynomials in part. As example we study the case of a quadratic intrinsic potential between the particles. The problem may be important for the motion of three nucleons in a crystal channel.

Purpose: The purpose of this study was to assess the association of the knee flexion excursion to the vertical center-of-mass (COM) amplitude and to the lower-extremity muscle work during stance phase for subjects with knee osteoarthritis. Method: Twenty subjects scheduled for total knee replacement and 20 controls performed level walking during standard gait analysis. Dependent variables included stance-phase knee flexion excursion, vertical COM amplitude, and lower-extremity muscle work. Results: Compared to healthy control, subjects with knee osteoarthritis walked with significantly less stance-phase knee flexion and vertical COM excursion. Knee flexion excursion was found to have a strong positive correlation to vertical COM amplitude. The lower-extremity muscle work during single stance phase was found to have a moderate negative correlation to vertical COM amplitude. Conclusions: Osteoarthritis of the knee alters both the stance-phase knee flexion and vertical COM excursions. As these variables show a strong positive relation, efforts to restore stance-phase knee flexion based on the 3rd determinant of gait require a new justification.

In the computer world garment products need to be simulated on different virtual human bodies. In this paper we are going to change virtual human actors in a proportional way. As part of the work we design a user-friendly interface for a more intuitive input of body parameters. Curves, implemented as NURBS, create an effective/easy input method for the proportional reshaping task. Implementation of an automatic approach for computing an underlying skeleton was done, which enables us to reshape a virtual human. As body proportions are difficult to define, this paper researches on artistic methods to describe the symmetric and harmonious structures of human bodies. A flexible data structure is employed in order to traverse and access regional information efficiently. As a main goal of this work we designed a high level controller for body parts enabling proportional reshaping.

This study identifies the optimal crouched starting positions (elongated, medium, or bunched) from push-off to the first two steps. Seven elite sprinters were recruited as participants in this study (aged: 21$\pm$2 years). A high-speed camera (250Hz) was used to collect motion-based images on a sagittal plane. Kwon3D (software) was used to analyze the center of mass (COM) movement, step length, foot linear velocity, take-off angle, and trunk angle. Participants were tested in a 60m sprint for bunched, medium, and elongated starting positions. A one-way analysis of variance (ANOVA) ($\alpha =0.05$) with repeated measures was performed to determine the difference in kinematics in the three crouched starting positions. The LSD comparison was applied to examine differences among pairs of means. Our results indicated that the medium starting position demonstrated a greater first step length and foot linear velocity when compared to the bunched starting position. In the first step toe-off, a lower COM vertical velocity was observed in the medium starting position when compared with the elongated starting position. This study concluded that the medium starting position was the ideal starting position.

The aim of this paper is to reduce the energy consumption of a humanoid by analyzing electrical power as input to the robot and mechanical power as output. The analysis considers motor dynamics during standing up and sitting down tasks. The motion tasks of the humanoid are described in terms of joint position, joint velocity, joint acceleration, joint torque, center of mass (CoM) and center of pressure (CoP). To reduce the complexity of the robot analysis, the humanoid is modeled as a planar robot with four links and three joints. The humanoid robot learns to reduce the overall motion torque by applying Q-Learning in a simulated model. The resulting motions are evaluated on a physical NAO humanoid robot during standing up and sitting down tasks and then contrasted to a pre-programmed task in the NAO. The stand up and sit down motions are analyzed for individual joint current usage, power demand, torque, angular velocity, acceleration, CoM and CoP locations. The overall result is improved energy efficiency between 25–30% when compared to the pre-programmed NAO stand up and sit down motion task.

The dynamic walking stability of biped robot is a challenging research topic. In this paper, the fuzzy controller on zero movement point (ZMP) criterion is implemented to maintain the balance of dynamic walking. We designed a force sensitive resistor (FSR) sensor circuits to collect information from the sensors for the ZMP trajectory tracking. The robot walking has an imbalance when the ZMP shows the risk of moving out the footprint. The fuzzy controller is provided to drive the ZMP inside the ZMP reference area, by adjusting a suitable angle for the ankle and hip joint. In order to determine the ZMP reference, we compute the inverse kinematic and Jacobian coordinates from the biped robot model. In this research, we also introduce the biped robot configuration for control dynamic walking. A user interface is designed to conventionally observe the ZMP trajectory generation. The experimental results for stability of dynamic walking are presented to appreciate the proposed method.

In this paper, we study the $n$-body problem in the Poincaré upper half-plane ${ℍ}_R^2$, where the radius $R$ of the Poincaré disk is fixed. We introduce a new potential to derive the condition for hyperbolic relative equilibria on ${ℍ}_R^2$. We analyze the relative equilibrium of positive masses moving along geodesics under the $\text{SL}(2,ℝ)$ group. This result is utilized to establish the existence of relative equilibria for the $n$-body problem on ${ℍ}_R^2$ for $n=2$ and $n=3$. We revisit previously known results and uncover new qualitative findings on relative equilibria that are not evident in an extrinsic context. Additionally, we provide a simple expression for the center of mass of a system of point particles on a two-dimensional surface with negative constant Gaussian curvature.

In this study, we focus on the concept of weightlessness in an experiment that involves magnetic forces, and discuss the motion of objects and the movement of a system’s center of mass from the perspective of inertial observer.

Knowledge of the control of the body's dynamic stability in patients with knee osteoarthritis (OA) is helpful for the management of these patients and for the evaluation of treatment outcomes. The purpose of the current study was to investigate the dynamic stability of patients with knee OA during level walking using variables describing the motion of the body's center of mass (COM) and its relationship to the center of pressure (COP). Kinematic and kinetic data during level walking were obtained from 10 patients with bilateral knee OA and 10 normal controls using a motion analysis system and two forceplates. Compared to the normal controls, patients with knee OA exhibited normal COM positions and velocities at key instances of gait but with significant changes in COM accelerations. In the sagittal plane, adjustments to the anterioposterior acceleration of the COM throughout the complete gait cycle were needed for better control of the COM during the more challenging latter half of single leg stance. Diminished A/P COM–COP separation was also used to maintain body stability with reduced joint loadings. In the frontal plane, this was achieved by increasing the acceleration of the body's COM towards the stance leg. The more jerky motion of the body's COM observed may be a result of reduced ability associated with knee OA in the control of the motion of the COM. Strengthening of the muscles of the lower extremities, as well as training of the control of the COM through a dynamic balance training program, are equally important for the dynamic stability of patients with knee OA.

Powered prosthetic feet (PPF) are designed to provide transtibial amputees (TTA) with active propulsion and range of motion similar to that of the biological limb. Previous studies have demonstrated the PPF’s ability to increase TTA walking speeds while reducing the energetic costs, however, little is known about its effects on dynamic balance control. The purpose of this pilot study was to assess dynamic balance control in TTA subjects during level ground walking and obstacle-crossing tasks. Control subjects ($n=6$) and TTA subjects ($n=4$) were instructed to complete a series of functional walking tasks. The TTA subjects completed the walking protocol twice, first in their passive energy-storing prosthetic foot (ESPF) and again in the prescribed PPF after two weeks of acclimation. Motion data were collected via a 10-camera system with a 53-marker and 15-segment body model. Whole body medial-lateral center of mass motion (displacement and peak velocity) was analyzed and used as a functional indicator of dynamic balance control. Findings indicate no difference in the dynamic balance control of TTA wearing the PPF compared to the ESPF. However, there was an observed trend of walking speed and obstacle height affecting balance control within the groups.

Falling is one of the leading causes of accidental injury and death among elderly adults and construction workers, with costs exceeding US$31 billion each year. Having good balance reduces the likelihood of falling — therefore it is important to determine which possible factors might influence balance. The purpose of this study was to determine if consuming three different types of breakfast altered blood glucose levels in such a way that young healthy individual’s balance control was compromised. Balance was then measured while the subjects completed single- and dual-task standing trials with eyes open and closed. Although changing blood glucose did alter quiet standing balance — as measured by the separation distance between the COG and COP, the velocity of the COM, and the total distance traveled by the COG and COP along the anterior–posterior (AP) and medial–lateral (ML) axes — the results were contradictory to what was hypothesized. Subjects with lower blood glucose swayed less than those with higher blood glucose. This could potentially be due to the habitual skipping of breakfast in young adults. Though the changing of blood glucose did influence quiet standing balance of young healthy adults, it was not in a way which increased the risk of falling.

The purpose of this study is to evaluate the sway areas of the center of pressure (COP) and the inclination angles between the center of mass (COM) and COP among elderly subjects with and without training in Chinese traditional exercises, including Tai Chi (TC) and Yuanji-Dance (YD). Additionally, this study investigates the electromyographic (EMG) activities during walking across these groups. The current study employed a cross-sectional study design. Twenty-seven healthy participants aged 45–70 years old were recruited from the local community in this study. TC group and YD group should have regular exercise training for at least two years, respectively. In the first part of this study, each subject of three groups (TC, YD and CON) was asked to walk at a self-selected speed on an 8 m walkway for gait analysis. Maximum center of mass–center of pressure (COM–COP) inclination angles in the sagittal plane and frontal plane were calculated. The EMG activity was recorded bilaterally from four muscles of the lower limbs including quadriceps, hamstring, tibialis anterior and gastrocnemius. In the second part, each subject was guided to perform four tandem static balance tests with the dominant leg leading on a force plate. The time-varying COP positions and the sway area of the COP were calculated from the ground reaction force data. A one-way ANOVA was conducted to compare walking variables between groups, and a two-way repeated measures ANOVA was used to evaluate the effects of group (between-group) and conditions (within-group) on the variables of the static tests. There were no significant differences in the maximum COM–COP inclination angles in anterior– posterior ($p$ = 0.06) and medial–lateral ($p$ = 0.15) directions as well as the EMG activities ($p$ > 0.05) among the TC, YD and CON groups. For static balance test, the TC group showed decreased excursion of COP in anterior– posterior direction and sway area compared with the CON group ($p$ < 0.01). For the YD group, decreased excursion of COP in the anterior–posterior direction during tandem stance on the soft surface was found ($p$ < 0.01). Moreover, the YD group showed decreased sway areas of COP compared with the CON group ($p$ < 0.01). The findings show that the TC group demonstrated smaller sway areas compared to the YD group, indicating that TC training may be especially effective in enhancing the static standing balance. However, there were no significant differences in the anterior–posterior and medial–lateral COM–COP inclination angles during walking among the TC, YD, and control groups. This result suggests that the training effects of TC and YD may not significantly impact the dynamic balance or the muscle activities observed during level walking.

Coupled elastic actuation has been proven to be a simple and effective method to realize natural biped walking. However, former researches found it hard to achieve high speed merely by adjusting control parameters. For the purpose of realizing fast walking in this method, we put forward a simple approach: moving CoM(center of mass) forward. Through numerical simulation, we found that a positive lateral offset of CoM could effectively increase walking speed by enlarging step length and shortening step period, both of which result from the reduction of swing leg retraction. To testify the simulation results, experiments based on a prototype were conducted. The dimensionless speed of the robot changes from 0.264 to 0.424 as CoM moves forward, which confirms our speed-increasing strategy.