Circular Motion Research Articles

Different right ventricular mechanics in atrial and ventricular secondary tricuspid regurgitation and their prognostic role. A multicentric three-dimensional echocardiography study

Abstract Background/Introduction Secondary tricuspid regurgitation (STR) can develop from markedly different etiologies. Both progressive dilation and dysfunction of the right atrium (atrial phenotype, ASTR), and adverse right ventricular (RV) remodeling (ventricular phenotype, VSTR) may result in STR. RV function is a major determinant of outcome in patients with STR. However, data about how RV function adapts to ASTR and VSTR are scarce, and the prognostic implications of RV mechanics in ASTR and VSTR remain to be clarified. Purpose Accordingly, we aimed to investigate the RV mechanical patterns in ASTR and VSTR and to examine their prognostic role using three-dimensional (3D) echocardiography. Methods We enrolled 192 patients with STR (60% women) who underwent clinically indicated transthoracic echocardiography in a multicentric prospective observational study. The primary outcome was defined as a composite of heart failure hospitalization or cardiac death. STR etiology was assessed based on the TVARC criteria (ventricular STR n=134, atrial STR n=58). STR severity was categorized using STR effective regurgitant orifice area according to current guidelines. We assessed RV function by measuring the tricuspid annular plane systolic excursion (TAPSE) by M-mode echocardiography and RV ejection fraction (EF) by 3D echocardiography. In addition, we imported the 3D RV meshes into the ReVISION software package (Argus Cognitive, Inc, Lebanon, USA) to quantify the relative contribution of the longitudinal (LEFi), radial (REFi), and anteroposterior motion components (AEFi) to total RV EF. Results ASTR and VSTR patients had comparable TAPSE (17±5 mm vs. 18±5 mm, p=0.10), while RV EF was significantly higher in ASTR (54±7% vs. 47±10% p<0.001). Although LEFi (0.37±0.08 vs. 0.38±0.10, p=0.95) and AEFi (0.45±0.08 vs. 0.44±0.11, p=0.53) were comparable between ASTR and VSTR, REFi was significantly lower in VSTR (0.52±0.09 vs. 0.47±0.12, p<0.01). RF EF was comparable among STR severity grades (mild vs. moderate vs. severe: 50±11 vs. 49±9 vs. 50±10%, respectively, p=0.85). Conversely, LEFi was significantly higher in mild and moderate STR vs severe STR (0.39±0.08 vs. 0.39±0.09 vs. 0.35±0.10, respectively, p=0.04). Using multivariable Cox regression based on variables significant in the univariate analysis, REFi was a significant independent predictor of outcome in the entire cohort (hazard ratio: 0.978 [CI, 0.959-0.999], p= 0.037). Conclusions Using 3D echocardiographic assessment, ASTR and VSTR patients demonstrated significant differences in the RV mechanical pattern, with a lower contribution of the radial contraction in the case of ventricular STR etiology. While RV EF was comparable between STR severity grades, the relative importance of the longitudinal motion significantly differed. Notably, the relative contribution of radial motion to RV function demonstrated independent prognostic value in patients with STR.RV mechanics in STR severity stages

Acute changes in right ventricular geometry and function following transcatheter tricuspid valve interventions

Abstract Background Little is known about acute changes in right ventricular (RV) function and geometry following transcatheter tricuspid edge-to-edge repair (T-TEER) or transcatheter tricuspid valve replacement (TTVR). Pressure-strain-volume loop-derived myocardial work metrics showed associations with myocardial energetics and contractility in conditions accompanied by volume overload, suggesting their potential utility in patients with tricuspid regurgitation (TR). Purpose To define acute changes in RV volumes and RV myocardial work following T-TEER and TTVR using conventional and pressure-strain-volume derived RV work metrics. Methods In this multicenter, observational study, 3D echocardiographic datasets and invasively acquired RV pressures were collected before and after transcatheter tricuspid valve procedure. Using dedicated software (ReVISION, Argus Cognitive) 3D RV volumes and strains were quantified and decomposed to longitudinal, radial and anterio-posterior motion. Forward stroke volume (SV) was calculated by subtracting TR volumes from RV 3D end-diastolic volume (EDV) and end-systolic volume (ESV) difference. Three-dimensional pressure-strain-volume loops were constructed and global RV work-index (RV-Wi) was calculated. Changes in RV parameters before and after the intervention were compared using paired-samples t test. Results Of 37 patients included in this study (65% male), 20 underwent T-TEER and 17 underwent TTVR. Compared to T-TEER patients, patients undergoing TTVR had higher prevalence of torrential TR at baseline but also achieved a higher reduction in TR volumes after the intervention (44 ± 11 ml vs 60 ± 16ml; p = 0,001). Following T-TEER there was a significant reduction in RV EDV (240 ± 93 ml vs 200 ± 80 ml; p < 0.001) and increase in SV (55 ± 34 ml vs 68 ± 26 ml; p = 0.036). Following TTVR there was a significant increase in RV ESV (121 ± 46 vs 146 ± 48, p = 0.003) and no significant change in SV (47 ± 24 ml vs 55 ± 20 ml; p = 0.143). There was significant reduction in RV strain and ejection fraction (EF) (all p < 0.001) primarily driven by reduction of radial motion component in both groups. RV-Wi increased in 35% (7/20) of T-TEER patients and in 18% of (3/17) TTVR patients. Conclusion An acute reduction in RV EF was observed in all patients and was mainly caused by decrease in RV EDV in T-TEER patients and increase in RV ESV in TTVR patients. Despite decrease of conventional metrics of RV function in both groups, an increase in RV-Wi was observed in 27% of all patients.Baseline and follow-up characteristicsCentral Figure

On the problem of optimal control of rotation axis reorientation of a spacecraft

Various variants of the formulation of optimal control problem of the reorientation of the axis of dynamic symmetry of the spacecraft (spacecraft), which is the axis of rotation, are considered. It is assumed that the solution to this problem should be found in the class of movements with one directional (flat) rotation, provided that before and after the reorientation of the axis of rotation, the angular velocity of the spacecraft is the same. In this case, the angular motion of the spacecraft is controlled according to the "rotary jet engine" scheme, when the control moment is limited by the ellipsoid of rotation. The corresponding mathematical model of spacecraft motion for the control problem under consideration is given. In addition to the formulation of the problem of the steepest reorientation of the axis of rotation of the spacecraft, the optimal control problem is also formulated, for which optimal control for the full control moment is found. In order to analyze the formulation of the problem under consideration, the results of its reduction to the boundary value problem and to the isoperimetric variational problem are also presented.

Influence of field mass and acceleration on entanglement generation

We explore the entanglement dynamics of two detectors undergoing uniform acceleration and circular motion within a massive scalar field, while also investigating the influence of the anti-Unruh effect on entanglement harvesting. Contrary to the conventional understanding of the weak anti-Unruh effect, where entanglement typically increases, we observe that the maximum entanglement between detectors does not exhibit a strict monotonic dependence on detector acceleration. Particularly at low accelerations, fluctuations in the entanglement maxima show a strong correlation with fluctuations in detector transition rates. We also find that the maximum entanglement of detectors tends to increase with smaller field mass. Novelly, our findings indicate the absence of a strong anti-Unruh effect in (3+1)-dimensional massive scalar fields. Instead, thermal effects arising from acceleration contribute to a decrease in the detector entanglement maximum.

Neo-Hookean modeling of nonlinear coupled behavior in circular plates supported by micro-pillars

In the contemporary era, the enhancement of wearable capacitive sensors is achieved through the utilization of polymeric micropillars as filler materials between electrode plates. To gain a deeper understanding of the dynamic response of the system, nonlinear coupled governing equations of a circular microplate motion resting on an array of polymeric micropillars have been derived. These equations are used to model the system’s behavior. In addition, the squeezing motion of the micro-pillars is characterized using the incompressible Neo-Hookean model. Both static and dynamic responses, including transient and steady-state solutions, are investigated in detail by discretizing over spatial coordinates using a weak formulation approach. A frequency response analysis is conducted using a continuation-based method. This entails expanding the steady-state solution using a Fourier transform and employing the energy balance principle. The unknown coefficients of the expansion series are calculated using a gradient descent-based learning approach that is physically motivated. Furthermore, a dynamic step size strategy for frequency increments is employed to effectively follow the solution path. This strategy is implemented via the ARC length method. In this study, we examine the impact of varying PDMS (polydimethylsiloxane) hydrogel mechanical and geometrical configurations. It can be reasonably concluded that the mechanical properties of the pillars and the geometrical configuration of the circular plate and micropillars have a significant impact on the maximum tolerable pressure, fast transient response, and frequency response analysis.

Energy Evolution in the Progenitor of Galaxy Shells: A Semi-analytical Model

The stellar shells surrounding an elliptical galaxy, as remnants of a dwarf galaxy disrupted during merging, reveal the distribution of energy and angular momentum of the progenitor dwarf galaxy. We develop a semi-analytical model to describe the changes in energy ΔE i and angular momentum ΔLz i for particles during the first infall. We show that these changes, induced by the self-gravity of the progenitor, are important in broadening the initial energy distribution of the Plummer or Hernquist progenitor model. Consequently, these changes are crucial in shaping the shells. In the freefall stage following the disintegration of the progenitor potential, particles are no longer bound by self-gravity but move within the gravitational potential of the target galaxy. We investigate the relationship between the radial period and the energy of particles undergoing radial motion. We show that an accurate model of the energy range of the dwarf galaxy at disruption is essential to predict the number of observable shells.

Hysteresis compensation and decoupling control of an XYΘ-type flexure-based mechanism via inverse hysteresis-coupling hybrid modeling

Planar positioning systems are widely utilized in micro and nano applications. The challenges in modeling and control of XYΘ flexure-based mechanisms include hysteresis of the piezoelectric actuators, couplings among the input axes, and coupled linear and angular motions of the end effector. This paper presents an inverse hysteresis-coupling hybrid model to account for such hysteresis and couplings. First, a specially designed kinematic chain is adopted to transfer the pose of the end effector into the linear motions at three prismatic joints. Second, an inverse hysteresis-coupling hybrid model is developed to linearize and decouple the system via a multilayer feedforward neural network. A fractional-order PID controller is also integrated to improve the motion accuracy of the overall system. Experimental results demonstrate that the proposed method can accurately control the motion of the end effector with improved accuracy and robustness.

Nonlinear vibro-acoustic analysis of an axially moving submerged circular cylindrical shell

In this study, the nonlinear vibro-acoustic dynamics and stability of doubly-clamped axially moving cylindrical shell are investigated. The exterior surface of the shell is in contact with fluid and subjected to oblique incident plane sound wave. Donnell’s nonlinear shallow shell theory is used to derive the nonlinear partial differential equation of the cylindrical shell for the radial motion. The Galerkin method is employed to discretize the equations of motion into the set of coupled nonlinear nonhomogeneous ordinary second order differential equations. Considering both driven and companion modes, Multiple Scales Method is used to obtain the response of the system. The effects of sound level, incident angle and axially velocity on the frequency response of the system are studied. The results show that, with increase in the shell velocity transmission loss of the circular shell increases. In addition, at low shell axial velocities simultaneous excitation of the driven and companion modes occurs.

Does cranial cruciate ligament repair by tibial plateau leveling osteotomy surgery restore dog’s natural kinematics? – A case series

Tibial plateau leveling osteotomy (TPLO) serves as an effective method of functional stabilization for treating cranial cruciate ligament (CrCL) deficiency. It is not clear if TPLO could restore the natural kinematics of the stifle, hip, and tarsal joints of the affected limb during walking. The hind limb motion between TPLO cases and control groups in eight adult dogs (4 French Bulldogs and 4 Pit Bull Terrier) was recorded by a motion capture system. Three-dimensional (3D) angular motions of the hip, stifle, and tarsal joints—including flexion-extension, abduction-adduction, and rotations—were computed and compared. Significant differences in joint kinematics were observed between TPLO cases and controls. In Case 1, the TPLO case in the French Bulldog showed differences in hip, stifle, and tarsal flexion-extension, abduction-adduction, and internal-external rotation. Asymmetries between affected and unaffected limbs were also detected in hip and stifle motions (up to 43° in some cases). Similar patterns of differences were found in Pit Bull Terriers Case 2 and Case 3, with significant variations in hip, stifle, and tarsal movements. Case 3 did not show hip asymmetries, but notable stifle and tarsal asymmetries were observed. The general daily activity performance for French Bulldogs and Pit Bull Terriers that underwent TPLO procedures was positive. The general daily restricted activity performance for the French Bulldog and Pit Bull Terriers that underwent TPLO procedures was positive. Our findings suggested that natural hind limb kinematics during gait was not restored in TPLO hind limb cases in both breeds.

UWB/IMU integrated indoor positioning algorithm based on robust extended Kalman filter

Abstract As a fundamental method for integrated indoor positioning, Ultra wideband (UWB)/ Inertial Measurement Unit (IMU) offers more stable performance compared to separate UWB sensor and IMU sensor positioning and uses the least squares (LS) and extended Kalman filter (EKF) for positioning processing, however, the performance of conventional LS and EKF will be seriously affected when the contamination rate of measurement noise is high. To address this problem, this paper proposes a robust extended Kalman filter (REKF) based algorithm for robot-integrated indoor positioning, which combines UWB and IMU positioning methods to obtain a more robust system performance and optimal positioning accuracy. In this paper, a vehicle equipped with a UWB/IMU sensor and four anchor points is set up to perform linear, circular, and trajectory motions in an experimental environment with visible obstacles. The experimental results show that compared with EKF, REKF improves the localization precision and accuracy in the three motions by 20.98%, 35.51%, and 47.06%, respectively. REKF effectively improves the accuracy and robustness of the robot’s indoor positioning, and provides an improved and practical method for integrated indoor positioning algorithms to make indoor positioning more accurate and reliable.

Effect of Cognitive Decline on Mandibular Movement during Mastication in Nursing Home Residents.

Background: Many studies have reported on the relationship between cognitive and masticatory functions. However, it remains unclear how the mandibular movements change during chewing in facility residents as dementia progresses. This study aimed to investigate the relationship between a kinematic analysis of mandibular movement during mastication and cognitive function in facility residents. Methods: Sixty-three participants were included from two long-term care facilities. The primary outcome variable was the kinematic data of mandibular movement during mastication. The participants chewed rice crackers, and their faces were recorded during this motion. The partial correlation coefficient between kinematic data and cognitive function was calculated. Furthermore, group comparisons were performed after dividing the participants into three groups based on their cognitive function. Results: Circular motion frequency was significantly correlated with the ABC dementia scale, even after adjusting for the appendicular skeletal muscle index, Eichner index, and short-form mini-nutritional assessment. The cycle and circular motion frequencies were markedly lower in the severe dementia group than in the mild dementia group. Conclusions: With declining cognitive function, mandibular movements during mastication decrease in circular motion and increase in linear motion. Additionally, our results suggested that residents with severe cognitive impairment had more linear mandibular motions during mastication than those with mild cognitive impairment. This may make it more difficult for residents with cognitive decline to ingest normal solid foods.

Effect of asymptomatic intervertebral flexion patterns on lumbar disc pressure: A finite element analysis study.

Movement patterns may be a factor for manipulating the lumbar load, although little information is yet available in the literature about the relationship between this variable and intervertebral disc pressure (IDP). A finite element model of the lumbar spine (49-year-old asymptomatic female) was used to simulate intervertebral movements (L2-L5) of 127 asymptomatic participants. The data from participants that at least completed a simulation of lumbar vertebral movement during the first 53% of a movement cycle (flexion phase) were used for further analyses. Then, for each vertebral angular motion curve with constant spatial peaks, different temporal patterns were simulated in two stages: (1) in lumbar pattern exchange (LPE), each vertebral angle was simulated by the corresponding vertebrae of other participants data; (2) in vertebral pattern exchange (VPE), vertebral angles were simulated by each other. The k-mean algorithm was used to cluster two groups of variables; peak and cumulative IDP, in both stages of simulations (i.e., LPE and VPE). In the second stage of the simulation (VPE), Kendall's tau was utilized to consider the relationship between different temporal patterns and IDPs for each individual lumbar level. Cluster analyses showed that the temporal movement pattern did not exhibit any effect on the peak IDP while the cumulative IDP changed significantly for some patterns. Earlier involvement in lumbar motion at any level led to higher IDP in the majority of simulations. There is therefore a possibility of manipulating lumbar IDP by changing the temporal pattern with the same ROM, in which optimal distribution of the loads among lumbar levels may be applied as preventive or treatment interventions. Evaluating load benefits, such as load, on biomechanically relevant lumbar levels, dynamically measured by quantitative fluoroscopy, may help inform interventional exercises.

Phase-modulation-induced reconfigurable rotating photonic lattices in atomic vapors.

We propose a method to prepare optically induced rotating hexagonal and honey-comb photonic lattices by employing the phase modulated three-beam interference in atomic vapors with electromagnetically induced transparency. The phase differences among the three beams are dynamically elaborated to synthesize the circular motion (in transverse dimensions) of waveguides in the photonic lattices. Further, we verify this model experimentally in the case of low-speed modulation. A weak Gaussian probe field is sent into the constructed helical photonic lattices to image their structures under electromagnetically induced transparency (EIT). The motion trajectories of the sites on the discretized output patterns exhibit repeated circles, advocating the formation of rotating lattices. By introducing phase modulations to involved beams, we provide a continent way for producing transverse motions in waveguide arrays with reconfigurability in rotational direction, radius, and speed. This work looks forward to promising applications in topological photonics with great popularity.

The penetration efficiency of a dissolved model drug into hair follicles depends on the concentration of added nanoparticles.

Hair follicles have recently emerged as promising drug delivery targets and gates for skin penetration. The so-called ratchet effect, which is based on an interaction between the hair shaft surface, the intrafollicular stratum corneum and nanoparticles, has proven to be very effective for the transport of active ingredients. Especially the nanoparticle-assisted decolonization of hair follicles constitutes an interesting new area of application. In a recently published work it was shown that small molecules as well as macromolecules solved in an outer phase of a formulation can be transported into the deeper parts of the hair follicles by adding nanoparticles to the formulation. In this case the nanoparticles constitute an entity independent of the drug and the transport is hypothesized to be based on an adhesion effect. In the present work, we focused on the impact of the particle concentration in the formulation on the transport efficiency of the model drug fluorescein sodium into hair follicles utilizing an ex vivo porcine skin model. It was observed that a particle concentration of 4% significantly enhances the transport efficiency of fluorescein as compared to 2% particle concentration. Doubling the concentration to 8% did not significantly increase the penetration depth. The effect evolved more efficiently when using 4Hz circular motion massage as compared to 100Hz oscillating massage. These results deliver interesting information on the optimal formulation as well as application parameters for a future application in clinical studies for e.g. skin antisepsis purposes.

Ovarian cancer cells exhibit diverse migration strategies on stiff collagenous substrata

In homoeostasis, the shape and sessility of untransformed epithelial cells are intricately linked together. Variations of this relationship in migrating cancer cells as they encounter different microenvironments are as yet ill-understood. Here, we explore the interdependency of such traits in two morphologically distinct invasive ovarian cancer cell lines (OVCAR-3 and SK-OV-3) under mechanically variant contexts. We first established a metric toolkit that assessed traits associated with cell motion and shape, and rigorously measured their dynamical variation across trajectories of migration using a Shannon entropic distribution. Two stiffness conditions on polymerized Collagen I with Young’s moduli of 0.5 kPa (soft) and 20 kPa (stiff) were chosen. Both the epithelioid OVCAR-3 and mesenchymal SK-OV-3 cells on soft substrata exhibited slow and undirected migration. On stiff substrata, SK-OV-3 showed faster persistent directed motion. Surprisingly, OVCAR-3 cells on stiffer substrata moved even faster than SK-OV-3 cells but showed a distinct angular motion. The polarity of SK-OV-3 cells on stiff substrata was well-correlated with their movement, whereas for OVCAR-3, we observed an unusual ‘slip’ behavior, wherein the axes of cell shape and movement were poorly correlated. While SK-OV-3 and OVCAR-3 showed greater mean deformation on stiffer substrata, the latter was anti-correlated with variation in angular motion or the mean deviation between shape and motility axis for SK-OV-3 but poorly correlated for OVCAR-3. Moreover, on softer substrata OVCAR-3 and SK-OV-3 were relatively rigid but showed greater shape variation (with OVCAR-3 showing a higher fold change) on stiffer substrata. Our findings suggest that greater deformability on stiffer milieu allow epithelioid cells to overcome constraints on the congruence in axis of shape and motion seen for mesenchymal cells and display distinct motile behaviors across this phenotypic spectrum.

Gaseous Dynamical Friction on Elliptical Keplerian Orbits

We compute the gaseous dynamical friction force experienced by massive perturbers on elliptical Keplerian orbits. Using linear perturbation theory, we investigate the density wake morphology, dynamical friction force, and secular orbital evolution for massive single perturbers as well as equal-mass binaries embedded in a homogeneous, static medium. In all cases, the rate of change in the semimajor axis is found to be negative (as expected), whereas the rate of change in eccentricity is negative for strictly subsonic trajectories and positive for strictly supersonic trajectories. Transonic orbits can experience both positive and negative torques during the course of an orbit, with some growing in eccentricity and others circularizing. We observe all initial orbits becoming highly supersonic and eccentric (over sufficiently long timescales) due to a relentless semimajor axis decay increasing the Mach number and subsequent eccentricity driving. We compare our findings to previous studies for rectilinear and circular motion while also making our data for the evolution of Keplerian orbits available.

Flow field analysis of newtonian fluid flow induced by planetary and radial motion of drill string

Abstract At present, in the process of oil drilling, the drill string is an essential downhole drilling tool. It is immersed in the hole filled with drilling fluid for a long time, and it is driven by the rotation of the rotary table to drill down. In this process, the drill string will not only rotate around its axis but also may rotate around the axis of the hole and produce radial motion. It is important to study the flow law of Newtonian fluid flow induced by drill string movement, which can effectively reduce drilling accidents caused by drill string vortex and buckling, thus reducing economic losses. After research and analysis, the finite volume method, which has good applicability and obvious advantages, is used to discretize the established mathematical model, and the mathematical equation after discretization is obtained. By using MATLAB software, the flow field of Newtonian fluid induced by drill string rotation motion is analyzed, the axial velocity distribution diagram and tangential velocity distribution diagram are obtained, and the velocity flow diagram under different eccentricity conditions is drawn. It is found that secondary flow occurs only when the eccentricity reaches a certain distance requirement.

Prediction of Leakage Flow Rate and Blow-Down in Brush Seals via 2D CFD Simulation with Porosity Correction

Brush seals are extensively used in rotating equipment, such as gas turbines and compressors, providing effective sealing while accommodating radial, axial, and angular movements between components. In this study, the performance of brush seals with and without clearances was predicted through axisymmetric 2D computational fluid dynamic (CFD) simulations using a porous media model. Because the accurate modeling of a brush seal requires the appropriate porosity to be determined and the flow resistance to be calculated, a porosity correction was performed based on the brush seal’s geometry and pressure ratio. The corrected porosity was then used to calculate the flow resistance and the leakage flow rate was predicted. Based on the results, the corrected porosity significantly improved the accuracy of the previously unreliable leakage flow rate predictions, regardless of the presence of clearances. For cases with a clearance, the blow-down effect was determined through CFD simulations for the given geometry and was compared with experimental data. The leakage flow rate predictions were highly accurate, with a relative error of less than 5% across a pressure ratio range of 1.5–4.

PERTURBED MOTIONS OF A NEARLY DYNAMICALLY SPHERICAL RIGID BODY WITH A MOVABLE MASS SUBJECT TO CONSTANT BODY-FIXED TORQUE

The problem of motion of a rigid body about a fixed point is one of the classical problems of mechanics. The interest to the problems of the rigid body dynamics has increased in the second half of the XX century in connection with the development of rocket and space technologies. A spacecraft or satellite, while orbiting about its center of mass, experiences torques from forces of diverse physical nature. This includes torques generated by the motion of internal masses, which can arise from factors such as presence of rotating components (like rotors or gyroscopes), and the activities of crew members aboard the crew vehicle. The dynamics of rigid body incorporated moving masses is a significant focal point in classical mechanics. Extensive research is dedicated to investigating the rotation of a rigid body featuring motion of internal masses. It is assumed that the body contains a viscoelastic element that is modeled by a moving mass connected to the body by a strong damper. The moving mass model loosely attached elements in a space vehicles, which can significantly affect the vehicle’s motion about its center of mass during a long period of time. Some cases are considered of the motion of a rigid body containing internal masses connected to the body by means of elastic and dissipative elements. A number of works are devoted to the analysis of various problems of the dynamics of space vehicles containing internal movable masses. The paper develops an approximate solution by means of averaging method to the system of Euler’s equation terms for a nearly dynamically spherical rigid body containing a viscoelastic element under the action of constant body-fixed torque. We obtained the system of motion equations in the standard form which refined in square-approximation by small parameter. Asymptotic approach permits to obtain some qualitative results and to describe evolution of angular motion using simplified averaged equations and numerical solution. The main objective of this paper is to extend the previous results for the problem of motion about a center of mass of a rigid body under the influence of small internal torque (cavity filled with a fluid of high viscosity) or external torque (resistive medium). The importance of the results is in progress of moving mass control motion of spinning projectiles.

Orbital Precession in Janis–Newman–Winicour Spacetime

We have investigated the Janis–Newman–Winicour spacetime through three fundamental tests of theories of gravity, namely, gravitational lensing, perihelion shift, and redshift due to gravitational force. Focusing initially on the circular motion of a massive particle within the equatorial plane, the analysis disregards external scalar field interactions. The Janis–Newman–Winicour (JNW) spacetime’s unique parameters, mass (M) and the scalar parameter (n), are examined, revealing an intriguing relationship between the innermost stable circular orbit position of the test particle and the scalar field parameter. The study also explores photon motion around a gravitational object in JNW spacetime, revealing the expansion of the photon sphere alongside a diminishing shadow, influenced by the external scalar field. Despite these complexities, gravitational bending of light remains consistent with general relativity predictions. The investigation extends to perihelion precession, where the trajectory of a massive particle in JNW spacetime exhibits eccentricity-dependent shifts, distinguishing it from Schwarzschild spacetime. Finally, oscillatory motion of massive particles in JNW spacetime is explored, providing analytical expressions for epicyclic frequencies using perturbation methods. The study concludes with the application of MCMC analyses to constrain the JNW spacetime parameters based on observational data.