Minimum Moment Of Inertia Research Articles

Microarchitecture of the penis bone (baculum) of a seal: A 3D morphometric examination using synchrotron and laboratory micro-computed tomography.

We examined the ultrastructure of the mammalian os penis at the high-resolution synchrotron level. Previously, bacular microanatomy had only been investigated histologically. We studied the baculum of the harp seal (Pagophilus groenlandicus), in which the baculum varies more in size and shape than does a mechanically constrained bone (humerus). We (1) investigated the microarchitecture of bacula and humeri from the same seal specimens, and (2) described changes in bone micro- and macro-morphology associated with age (n = 15, age range = 1-35 years) and bone type. We analyzed cross-sectional geometry non-destructively through laboratory micro-computed tomography. We suggest that the midshaft may resist axial compression while the proximal region may resist torsion, based on measurements of cross-sectional and cortical areas, perimeter, ratio of maximum and minimum moments of inertia, and polar moment of inertia. In addition, midshaft bacula may be less mechanosensitive than humeri, based on microstructural variables (e.g., volume, surface area, diameter associated with lacunae and cortical porosity) analyzed across age groupings. Our findings related to the microarchitecture of the pinniped baculum provide a basis for further studies on development, mechanical properties, functions, and adaptations in this and other pinniped species. Our use of a multi-modal imaging approach was minimally destructive for reproducible and accurate comparison of three-dimensional bone ultrastructure. Such methods, coupled with multidisciplinary analyses, enable diverse studies of bone biology, life history, and evolution using museum collections.

CT-Scan-Based Approach for Turbine Blade Geometry Extraction

Abstract This paper presents a method for the assessment of the geometrical properties of the turbine blade after a long running time. This method uses a medical imaging device (CT-Scan) to provide segmentation images of the turbine blade. Image processing technique was employed to produce the cross-sectional properties such as area, centroid, minimum moment of inertia, maximum moment of inertia, and the angle of twist of the principal axes along the blade span. This geometrical information was produced using MATLAB code and validated against Image-J software data. This method can be used as a nondestructive method to evaluate the geometry of the turbine.

Pharmacologic Inhibition of Myostatin With a Myostatin Antibody Improves the Skeletal Muscle and Bone Phenotype of Male Insulin-Deficient Diabetic Mice.

Type 1 diabetes (T1D) is associated with low bone and muscle mass, increased fracture risk, and impaired skeletal muscle function. Myostatin, a myokine that is systemically elevated in humans with T1D, negatively regulates muscle mass and bone formation. We investigated whether pharmacologic myostatin inhibition in a mouse model of insulin-deficient, streptozotocin (STZ)-induced diabetes is protective for bone and skeletal muscle. DBA/2J male mice were injected with low-dose STZ (diabetic) or vehicle (non-diabetic). Subsequently, insulin or palmitate Linbits were implanted and myostatin (REGN647-MyoAb) or control (REGN1945-ConAb) antibody was administered for 8 weeks. Body composition and contractile muscle function were assessed in vivo. Systemic myostatin, P1NP, CTX-I, and glycated hemoglobin (HbA1c) were quantified, and gastrocnemii were weighed and analyzed for muscle fiber composition and gene expression of selected genes. Cortical and trabecular parameters were analyzed (micro-computed tomography evaluations of femur) and cortical bone strength was assessed (three-point bending test of femur diaphysis). In diabetic mice, the combination of insulin/MyoAb treatment resulted in significantly higher lean mass and gastrocnemius weight compared with MyoAb or insulin treatment alone. Similarly, higher raw torque was observed in skeletal muscle of insulin/MyoAb-treated diabetic mice compared with MyoAb or insulin treatment. Additionally, muscle fiber cross-sectional area (CSA) was lower with diabetes and the combination treatment with insulin/MyoAb significantly improved CSA in type II fibers. Insulin, MyoAb, or insulin/MyoAb treatment improved several parameters of trabecular architecture (eg, bone volume fraction [BV/TV], trabecular connectivity density [Conn.D]) and cortical structure (eg, cortical bone area [Ct. Ar.], minimum moment of inertia [Imin]) in diabetic mice. Lastly, cortical bone biomechanical properties (stiffness and yield force) were also improved with insulin or MyoAb treatment. In conclusion, pharmacologic myostatin inhibition is beneficial for muscle mass, muscle function, and bone properties in this mouse model of T1D and its effects are both independent and additive to the positive effects of insulin. © 2023 The Authors. JBMR Plus published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research.

Plasma Growth and Differentiation Factor 15 Predict Longitudinal Changes in Bone Parameters in Women, but Not in Men.

Bone fragility can progress with aging, but biomarkers to detect emerging osteopenia have not been fully elucidated. Growth/differentiation factor 15 (GDF-15) has pleiotropic roles in a broad range of age-related conditions, but its association with osteopenia is unknown. We examined the relationship between plasma GDF-15 levels and rate of change in bone parameters over 9 years of follow-up in 596 adults in the InCHIANTI study (baseline age, 65-94 years; women, 52.4%; mean follow-up, 7.0 ± 3.0 years). Plasma GDF-15 concentrations were measured using the 1.3k HTS SOMAscan assay. Eight bone parameters were measured in the right tibia by peripheral quantitative computed tomography; total bone density, trabecular bone density, medullary plus trabecular bone density, cortical bone density, total bone area, cortical bone area, medullary bone area, and minimum moment of inertia (mMOI). We ran sex-specific linear mixed-effect models with random intercepts and slopes adjusted for age, age-squared, education, body mass index, the rate of change in weight, smoking, sedentary behavior, cross-sectional areas of calf muscles and fat, 25-hydroxyvitamin D, parathyroid hormone, calcium, diabetes mellitus, and follow-up time. We found a significant association of "baseline GDF-15 × time" in models predicting cortical bone density and the mMOI in women, suggesting that the rates of decline in these bone parameters increased with higher GDF-15 (false discovery rate <0.05). Higher plasma levels GDF-15 predicted an accelerated decline in bone parameters in women, but was less associated in men. Furthermore studies are needed to understand the mechanisms underlying these sex differences.

Enhancement of evaluating flatfoot on a weight-bearing lateral radiograph of the foot with U-Net based semantic segmentation on the long axis of tarsal and metatarsal bones in an active learning manner

Robust labeling for semantic segmentation in radiographs is labor-intensive. No study has evaluated flatfoot-related deformities using semantic segmentation with U-Net on weight-bearing lateral radiographs. Here, we evaluated the robustness, accuracy enhancement, and efficiency of automated measurements for flatfoot-related angles using semantic segmentation in an active learning manner.A total of 300 consecutive weight-bearing lateral radiographs of the foot were acquired. The first 100 radiographs were used as the test set, and the following 200 radiographs were used as the training and validation sets, respectively. An expert orthopedic surgeon manually labeled ground truths. U-Net was used for model training. The Dice similarity coefficient (DSC) and Hausdorff distance (HD) were used to evaluate the segmentation results. In addition, angle measurement errors with a minimum moment of inertia (MMI) and ellipsoidal fitting (EF) based on the segmentation results were compared between active learning and learning with a pooled dataset.The mean values of DSC, HD, MMI, and EF of the average of all bones were 0.967, 1.274 mm, 0.792°, and 1.147° in active learning, and 0.964, 1.292 mm, 0.828°, and 1.186° in learning with a pooled dataset, respectively. The mean DSC and HD were significantly better in active learning than in learning with a pooled dataset. Labeling of all bones required 0.82 min in active learning and 0.88 min in learning with a pooled dataset.The accuracy and angle errors generally converged in both learning. However, the accuracies based on DSC and HD were significantly better in active learning. Moreover, active learning took less time for labeling, suggesting that active learning could be an accurate and efficient learning strategy for developing flatfoot classifiers based on semantic segmentation.

Feature Extraction and Retrieval of Ecommerce Product Images Based on Image Processing

The new retail is an industry featured by online ecommerce. One of the key techniques of the industry is the product identification based on image processing. This technique has an important business application value, because it is capable of improving the retrieval efficiency of products and the level of information supervision. To acquire high-level semantics of images and enhance the retrieval effect of products, this paper explores the feature extraction and retrieval of ecommerce product images based on image processing. The improved Fourier descriptor was innovatively into a metric learning-based product image feature extraction network, and the attention mechanism was introduced to realize accurate retrieval of product images. Firstly, the authors detailed how to acquire the product contour and the axis with minimum moment of inertia, and then extracted the shape feature of products. Next, a feature extraction network was established based on the metric learning supervision, which is capable of obtaining distinctive feature, and thus realized the extraction of distinctive and classification features of products. Finally, the authors expounded on the product image retrieval method based on cluster attention neural network. The effectiveness of our method was confirmed through experiments. The research results provide a reference for feature extraction and retrieval in other fields of image processing.

Conveyer-belt accidents in mining and metallurgy

The dynamic interaction between the mechanical and electrical drive parameters when damage suddenly appears in the mechanical part of a conveyer belt is investigated. The possibility of using the change in the motor’s electrical parameters as a diagnostic signal is assessed. A model for investigating the dynamic processes in the system consisting of the grid, the induction motor, and the conveyer belt is proposed. The grid and induction motor are described by a model of fourth-order state space, whose output is the torque at the motor shaft. The moments of inertia and pliability of the links between the elements in the mechanical part of the conveyer belt are determined. By gradually identifying the elements with the minimum moment of inertia and distributing their moments of inertia and pliabilities among the adjacent elements, we obtain a three-mass system simulating the mechanical part of the conveyer belt. This dynamic model is solved by means of Matlab Simulink software. The energy characteristics of the drive are determined in dynamic processes following a mechanical accident.

Exercise characteristics influence femoral cross-sectional geometry: a magnetic resonance imaging study in elite female athletes.

The associations between mid-femoral cross-sectional geometry and exercise characteristics were investigated in female athletes. The effects on bone geometry for weight-bearing sports with low-to-high-impact were greater than those for non-impact weight-bearing sports, whereas low-impact or high-strain-magnitude/low-strain-rate sports had less of an effect on bone geometry compared with higher-impact sports. Many previous studies have investigated tibial geometry in athletes; however, few studies have examined the associations between femoral cross-sectional geometry and exercise characteristics. The aim of this study was to investigate these relationships using magnetic resonance imaging (MRI) at the femoral mid-shaft. One hundred and fifty-three female elite athletes, aged 18-34 years, were classified into five groups based on the characteristics of their sports. Sports were considered non-impact (n = 27), low- or moderate-impact (n = 39), odd-impact (n = 38), high-strain-magnitude/low-strain-rate (n = 10), or high-impact (n = 39). Bone geometrical parameters, including cortical area, periosteal perimeter, and moment of inertia (bone strength index), were determined using MRI images. Higher-impact groups displayed bone expansion, with significantly greater periosteal perimeters, cortical areas (~37.3%), and minimum moments of inertia (I(min,) ~92.3%) at the mid-femur than non- and low-impact groups. After adjusting for age, height, and weight, the cortical area and I(min) of the low-impact and high-strain-magnitude/low-strain-rate groups were also significantly greater than those of the non-impact group. Higher-impact sports with high strain rates stimulated periosteal bone formation and improved bone geometry and strength indices at the femoral mid-shaft. Although our results indicate that weight-bearing sports are beneficial even if they are low impact, the effects of lower-impact or high-strain-magnitude/low-strain-rate sports on bone geometry were less pronounced than the effects of higher-impact sports at the femoral mid-shaft.

Bone Density, Structure and Strength, and Their Determinants in Aging Sprint Athletes

This study was undertaken to examine bone properties in masters sprinters of different ages and younger reference subjects. In addition, the association of sport-specific ground reaction force, muscle, training, and hormone characteristics with the bone parameters was evaluated in the athletes. Bone densitometric, structural, and strength parameters were assessed by peripheral quantitative computed tomography at the distal and midtibia in 83 male sprinters (40-85 yr) and 19 physically active referents (31-45 yr). Between-group differences were analyzed by ANCOVA with body mass and height as covariates. Bone values were generally greater in athletes than referents, the greatest differences being in bending strength of the tibia shaft as estimated by maximum moment of inertia (Imax). Among athletes, trabecular volumetric bone mineral density of distal tibia was 12% (P < 0.05) lower in the oldest (≥70 yr) versus youngest group, whereas the total bone mineral content, total cross-sectional area, and compressive bone strength index did not differ between the groups. At midtibia, no age group differences were present in the total bone mineral content, total cross-sectional area, cortical wall thickness, cortical volumetric bone mineral density, polar mass distribution, minimum moment of inertia, or maximum moment of inertia. After controlling for age, body mass, and height, most loading-related characteristics, knee extensor muscle thickness, and hormone concentrations correlated with the bone parameters. Multivariate regression models explained 12%-67% (mean, 47.5%) of the variance of the bone parameters. Mechanical power in the eccentric phase of the hopping and body mass were consistently the strongest independent predictors in the models. The results suggest that regular sprint training has positive (direction-specific) effects on bone strength and structure in middle- and older-aged athletes. Interindividual differences in bone traits seem to be due to combined effects of exercise loading, body size, and hormonal characteristics.

Characteristics of bone turnover, bone mass and bone strength in Spontaneously Diabetic Torii-Lepr fa rats

The Spontaneously Diabetic Torii-Lepr (fa) (SDT-fa/fa) rat is a new model of obese type 2 diabetes. The SDT-fa/fa rat shows obesity and hyperglycemia at a young age compared to the Spontaneously Diabetic Torii (SDT-+/+) rat; however, bone abnormalities in the SDT-fa/fa rat have not been investigated. The objective of the present study was to investigate the effects of obese type 2 diabetes on bone turnover, bone mass, and bone strength in the SDT-fa/fa rat. Sprague-Dawley rats were used as control animals, and SDT-+/+ rats were used as non-obese type 2 diabetic rats. Serum osteocalcin and urine deoxypyridinoline levels were decreased in SDT-fa/fa rats compared to control rats at a young age. SDT-fa/fa rats showed decreases in bone mineral density and bone mineral content of the whole tibia, and shortening of the tibia and femur compared to control and SDT-+/+ rats. Deterioration in bone geometrical properties of the femur midshaft such as cortical thickness and minimum moment of inertia, was observed in SDT-fa/fa rats compared to control and SDT-+/+ rats. Furthermore, trabecular bone volume of the distal femur was decreased in SDT-fa/fa rats compared to control rats. These negative effects on bone in SDT-fa/fa rats caused severe decreases in maximum load, stiffness, and energy absorption of the femur. In addition, serum levels of homocysteine, a candidate for bone fragility markers, were elevated in SDT-fa/fa rats compared to control and SDT-+/+ rats. In conclusion, the SDT-fa/fa rat may be a useful model to investigate bone abnormalities in obese type 2 diabetes.

A Comprehensive Regression Tree to Estimate Body Weight from the Skeleton*,†

The purpose of this research is to estimate actual body weight (in particular obesity) from the human skeleton. Known individuals (total n=187) were studied from the Bass Collection from the University of Tennessee, Knoxville. This research combines bone density, cross-sectional geometry of the femur and skeletal pathologies. Bone mineral density was calculated for the proximal femur. Three-dimensional bone surface models were created from computed tomographic scans. Cross-sectional geometry of the femur was calculated at five locations along the diaphysis. The pathologies analyzed were heel spurs, diffuse idiopathic skeletal hyperostosis (DISH), and tibial osteoarthritis. The best regression tree model included only four variables. The first split to estimate body weight was the minimum moment of inertia (I(y) ) at the distal femur, the second was midshaft width, then anteroposterior thickness at the proximal slice and the final split was the degree of DISH (SD 17.1-31.0 kg). The ability to estimate body weight from the skeleton is one more useful tool for the osteologist.

Effects of lifetime loading history on cortical bone density and its distribution in middle-aged and older men

We have reported previously that long-term participation of weight-bearing exercise is associated with increased QCT-derived cortical bone size and strength in middle-aged and older men, but not whole bone cortical volumetric BMD. However, since bone remodeling and the distribution of loading-induced strains within cortical bone are non-uniform, the aim of this study was to examine the effects of lifetime loading history on cortical bone mass distribution and bone shape in healthy community dwelling middle-aged and older men. We used QCT to assess mid-femur and mid-tibia angular bone mass distribution around its center (polar distribution), the bone density distribution through the cortex (radial distribution), and the ratio between the maximum and minimum moments of inertia ( I max/ I min ratio) in 281 men aged 50 to 79 years. Current (> 50 years) and past (13–50 years) sport and leisure time activity was assessed by questionnaire to calculate an osteogenic index (OI) during adolescence and adulthood. All men were then categorized into a high (H) or low/non impact (L) group according to their OI scores in each period. Three contrasting groups were then formed to reflect weight-bearing impact categories during adolescence and then adulthood: H–H, H–L and L–L. For polar bone mass distribution, bone deposition in the anterolateral, medial and posterior cortices were 6–10% greater at the mid-femur and 9–24% greater at mid-tibia in men in the highest compared to lowest tertile of lifetime loading ( p < 0.01– < 0.001). When comparing the influence of contrasting loading history during adolescence and adulthood, there was a graded response between the groups in the distribution of bone mass at the anterior-lateral and posterior regions of the mid-tibia (H–H > H–L > L–L). For radial bone density distribution, there were no statistically significant effects of loading at the mid-femur, but a greater lifetime OI was associated with a non-significant 10–15% greater bone density near the endocortical region of the mid-tibia. In conclusion, a greater lifetime loading history was associated with region-specific adaptations in cortical bone density.

Potential of First Arriving Signal to Assess Cortical Bone Geometry at the Hip with QUS: A Model Based Study

There is evidence that quantitative ultrasound (QUS) at the proximal femur involves waves propagating circumferentially in the cortical shell. These waves, in theory, convey information on bone geometrical and material characteristics and thus have the potential to improve fracture risk prediction. In this work, the time-of-flight (TOF) of the first arriving signal (FAS) that corresponds to waves propagating circumferentially is considered. The relationships between the TOF of the FAS and geometrical features of the femoral neck are investigated. Five neck cross-sections from 11 human femurs from females ( > 65 y) were extracted from 3-D X-ray quantitative computed tomography (XR-QCT) datasets. Geometrical parameters including cross-sectional area (CSA), minimum moment of inertia ( I min) and section modulus ( Z) were computed from femoral neck cross-section images. Two-dimensional numerical simulation of US propagation through femoral neck was performed and TOF of the FAS was estimated. TOF was best correlated with I min : R 2 = 0.82 ( p = 10 − 4 ; R M S E = 1390 m m 4 [ 13 % ]) in the region between proximal and mid-femoral neck and with Z : R 2 = 0.55 ( p < 10 − 2 ; R M S E = 480 m m 3 [ 17 % ]) and C S A : R 2 = 0.62 ( p < 5.10 − 3 ; R M S E = 22 m m 2 [ 7 % ]) in the mid-femoral neck. The results suggest that QUS has the potential to assess proximal femur strength based on estimates of geometrical properties of the cortical shell. (E-mail: julien.grondin@upmc.fr)

The rotation of Janus and Epimetheus

Epimetheus, a small moon of Saturn, has a rotational libration (an oscillation about synchronous rotation) of 5.9 ° ± 1.2 ° , placing Epimetheus in the company of Earth’s Moon and Mars’ Phobos as the only natural satellites for which forced rotational libration has been detected. The forced libration is caused by the satellite’s slightly eccentric orbit and non-spherical shape. Detection of a moon’s forced libration allows us to probe its interior by comparing the measured amplitude to that predicted by a shape model assuming constant density. A discrepancy between the two would indicate internal density asymmetries. For Epimetheus, the uncertainties in the shape model are large enough to account for the measured libration amplitude. For Janus, on the other hand, although we cannot rule out synchronous rotation, a permanent offset of several degrees between Janus’ minimum moment of inertia (long axis) and the equilibrium sub-Saturn point may indicate that Janus does have modest internal density asymmetries. The rotation states of Janus and Epimetheus experience a perturbation every 4 years, as the two moons “swap” orbits. The sudden change in the orbital periods produces a free libration about synchronous rotation that is subsequently damped by internal friction. We calculate that this free libration is small in amplitude (<0.1°) and decays quickly (a few weeks, at most), and is thus below the current limits for detection using Cassini images.

A study of evolution of spin-up mode of a satellite in the plane of its orbit

We investigate the mode of spinning up a low-orbit satellite in the plane of its orbit. In this mode the satellite rotates around its principal central axis of the minimum moment of inertia which executes small oscillations with respect to the normal to the orbit plane; the angular velocity of the rotation around this axis several times exceeds the mean orbital motion. Gravitational and restoring aerodynamic moments are taken into account in the satellite’s equations of motion. A small parameter characterizing deviation of the satellite from a dynamically symmetric shape is introduced into the equations. A two-dimensional integral surface of the equations of motion, describing quasi-steady-state rotations of the satellite close to cylindrical precession of the corresponding symmetrical satellite in a gravitational field, has been studied by the method of small parameter and numerically. Such quasi-steady-state rotations are suggested to be considered as unperturbed motions of the satellite in the spin-up mode. Investigation of the integral surface is reduced to numerical solution of a periodic boundary value problem of a certain auxiliary system of differential equations and to calculation of quasi-steady-state rotations by the two-cycle method. A possibility is demonstrated to construct quasi-steady rotations by way of minimization of a special quadratic functional.

One method of gravitational attitude control of a rotating satellite

The mode of spinning up a low-orbit satellite in the plane of its orbit is studied. In this mode, the satellite rotates around its longitudinal axis (principal central axis of the minimum moment of inertia), which executes small oscillations with respect to the normal to the orbit plane; the angular velocity of the rotation around the longitudinal axis is several tenths of a degree per second. Gravitational and restoring aerodynamic moments were taken into account in the equations of satellite’s motion, as well as a dissipative moment from eddy currents induced in the shell of the satellite by the Earth’s magnetic field. A small parameter characterizing deviation of the satellite from a dynamically symmetric shape and nongravitational external moments are introduced into the equations. A two-dimensional integral surface of the equations of motion, describing quasistationary rotations of the satellite close to cylindrical precession of the corresponding symmetrical satellite in a gravitational field, has been studied by the method of small parameter and numerically. We propose to consider such quasistationary rotations as unperturbed motions of the satellite in the spin-up mode.

Optimization of a Composite Rotor Blade using a Genetic Algorithm with Local Search

The material and ply angles of a fiber-reinforced plastic (FRP) rotor blade of a helicopter are optimized using a genetic algorithm (GA) with local search. The variation of the structural stiffness with material and ply angle is investigated. The aim of the optimization is to find an optimal stacking sequence that minimizes twist deformation. An optimum rotor blade is obtained using the ply angles as variables; failure, natural frequency, and minimum moment of inertia are used to constrain the optimization. The GA is employed as an optimization tool. A simplified local search is implemented in the final stage of optimization to reduce the searching time.

Aging bone in men and women: beyond changes in bone mineral density.

Using peripheral quantitative computed tomography (pQCT) we assessed trabecular and cortical bone density, mass and geometric distribution at the tibia level in 512 men and 693 women, age range 20-102 years, randomly selected from the population living in the Chianti area, Tuscany, Italy. Total, trabecular and cortical bone density decreased linearly with age ( p<0.0001 in both sexes), and the slope of age-associated decline was steeper in women than in men. In men, the cortical bone area was similar in different age groups, while in women older than 60 years it was significantly smaller by approximately 1% per year. The total cross-sectional area of the bone became progressively wider with age, but the magnitude of the age-associated increment was significantly higher in men than in women ( p<0.001). The minimum moment of inertia, an index of mechanical resistance to bending, remained stable with age in men, while it was significantly lower in older compared with younger women (0.5% per year). The increase in bone cross-sectional area in aging men may contribute to the maintenance of adequate bone mechanical competence in the face of declining bone density. In women this compensatory mechanism appears to be less efficient and, accordingly, the bone mechanical competence declines with age. The geometric adaptation of increasing cross-sectional bone size is an important component in the assessment of bone mechanical resistance which is completely overlooked, and potentially misinterpreted, by traditional planar densitometry.

The Mode of Gravitational Orientation for the International Space Station

The results of the determination of the uncontrolled attitude motion of the International Space Station during its unmanned flight in 1999 are presented. The data of onboard measurements of three components of the angular velocity are used for this determination. These data covering an interval of slightly less than one orbit were jointly processed by the least squares method, by integrating the equations of motion of the station relative to its center of mass. As a result of this processing, the initial conditions of the motion and the parameters of the mathematical model used were estimated. The actual motion of the station has been determined for 20 such intervals during April–November. Throughout these intervals, the station rotated about the axis of the minimum moment of inertia, the latter executing small oscillations relative to the local vertical. Such a mode, known as the mode of gravitational orientation of a rotating satellite or the mode of generalized gravitational orientation, was planned before the flight. The measurements were made to verify it. The quasistatic component of the microaccelerations aboard the station is estimated for this mode.

Uncontrollable Rotational Motion of the Mir Orbital Station

The results of determining the rotational motion of the Mir orbital station are presented for four long segments of its unmanned uncontrolled flight in 1999–2000. The determination was carried out using the data of onboard measurements of the Earth's magnetic field intensity. These data, taken for a time interval of several hours, were jointly processed by the least squares method with the help of integration of the equations of station motion relative to its center of mass. As a result of this processing, the initial conditions of motion and the parameters of the mathematical model used were evaluated. The technique of processing is verified using the telemetry data on angular velocity of the station and its attitude parameters. Two types of motion were applied on the investigated segments. One of them (three segments) presents a rotation around the axis of the minimum moment of inertia. This axis executes small oscillations with respect to a normal to the orbit plane. Such a motion was used for the first time on domestic manned orbital complexes. The second type of motion begins with a biaxial rotation which, in a few weeks, goes over into a motion very similar to the rotation around the normal to the orbit plane, but around the axis of the maximum moment of inertia.