Modeling the optimal reduction of the small angular velocity of a microsatellite using onboard magnetic coils

2016 ◽  
Author(s):  
V. V. Lyubimov ◽  
S. V. Podkletnova
Keyword(s):  
Angular Velocity ◽  
Magnetic Coils ◽  
Small Angular Velocity ◽  
Optimal Reduction

Stability of a Rigid Body With an Oscillating Particle: An Application of MACSYMA

1985 ◽  
Vol 52 (3) ◽  
pp. 686-692 ◽  
Author(s):  
L. A. Month ◽  
R. H. Rand
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Classical Problem ◽  
Moment Of Inertia ◽  
Model Parameters ◽  
Stability Chart ◽  
The Stability ◽  
Transition Curves ◽  
Minimum Moment ◽  
Small Angular Velocity

This problem is a generalization of the classical problem of the stability of a spinning rigid body. We obtain the stability chart by using: (i) the computer algebra system MACSYMA in conjunction with a perturbation method, and (ii) numerical integration based on Floquet theory. We show that the form of the stability chart is different for each of the three cases in which the spin axis is the minimum, maximum, or middle principal moment of inertia axis. In particular, a rotation with arbitrarily small angular velocity about the maximum moment of inertia axis can be made unstable by appropriately choosing the model parameters. In contrast, a rotation about the minimum moment of inertia axis is always stable for a sufficiently small angular velocity. The MACSYMA program, which we used to obtain the transition curves, is included in the Appendix.

Large Deformations of a Rotating Solid Cylinder for Non-Gaussian Isotropic, Incompressible Hyperelastic Materials

2000 ◽  
Vol 68 (1) ◽  
pp. 115-117 ◽  
Author(s):  
C. O. Horgan ◽  
G. Saccomandi
Keyword(s):  
Angular Velocity ◽  
Strain Energy ◽  
Large Deformations ◽  
Rotating Cylinder ◽  
Solid Cylinder ◽  
Hyperelastic Materials ◽  
Steady Rotation ◽  
Non Gaussian ◽  
Limiting Value ◽  
Small Angular Velocity

The purpose of this research is to investigate the steady rotation of a solid cylinder for a class of strain-energy densities that are able to describe hardening phenomena in rubber. It is well known that use of the classic neo-Hookean strain energy gives rise to physically unrealistic response in this problem. In particular, solutions exist only for a sufficiently small angular velocity. As the velocity approaches this limiting value, the analysis predicts that the rotating cylinder collapses to a disk. It is shown here that this nonphysical behavior does not occur when generalized neo-Hookean models, which exhibit hardening at large deformations, are used.

scholarly journals An Approximate Solution for Flow between Two Disks Rotating about Distinct Axes at Different Speeds

2007 ◽  
Vol 2007 ◽  
pp. 1-16 ◽  
Author(s):  
H. Volkan Ersoy
Keyword(s):  
Reynolds Number ◽  
Approximate Solution ◽  
Angular Velocity ◽  
Analytical Solution ◽  
Viscous Fluid ◽  
Approximate Analytical Solution ◽  
Velocity Difference ◽  
Small Angular Velocity

The flow of a linearly viscous fluid between two disks rotating about two distinct vertical axes is studied. An approximate analytical solution is obtained by taking into account the case of rotation with a small angular velocity difference. It is shown how the velocity components depend on the position, the Reynolds number, the eccentricity, the ratio of angular speeds of the disks, and the parameters satisfying the conditionsu=0andν=0in midplane.

scholarly journals Dynamical Friction Effects on the Motion of Stars in Rotating Spherical Clusters

1974 ◽  
Vol 62 ◽  
pp. 285-296
Author(s):  
A. S. Baranov ◽  
Yu. V. Batrakov
Keyword(s):  
Angular Velocity ◽  
Differential Equations ◽  
Density Distribution ◽  
Approximate Formula ◽  
Massive Stars ◽  
Dynamical Friction ◽  
Stellar Matter ◽  
Fixed Axis ◽  
Osculating Elements ◽  
Small Angular Velocity

Effects of dynamical friction on star orbits in a spherical cluster uniformly rotating with small angular velocity about a fixed axis are considered, deformations of the cluster due to the rotation being neglected. The test star is supposed to move in a noncircular restricted orbit under the influence of both the attraction of the cluster with the smoothed-out distribution of stellar matter and dynamical friction due to random encounters of the test star with other stars of the cluster.The approximate formula for dynamical friction has been deduced, the encounters being supposed to be the binary ones. The differential equations for the osculating elements of the star orbit have been obtained for the two cases of the density distribution - the uniform and the exponential ones. The numerical results demonstrate the complicated character of dynamical friction effects on the evolution of the orbit. The orbit tends to become circular, and its inclination decreases. These effects are proportional to the mass of the test star. This leads to the conclusion that dynamical friction contributes noticeably to the concentration of massive stars near the center of the cluster.

Kelvin–Helmholtz problem in a rotating Hall plasma

1980 ◽  
Vol 24 (2) ◽  
pp. 213-219 ◽  
Author(s):  
A. T. Granik
Keyword(s):  
Angular Velocity ◽  
Wave Vector ◽  
Shear Plane ◽  
Helmholtz Problem ◽  
Effects Of Rotation ◽  
Hall Plasma ◽  
The Stability ◽  
Special Case ◽  
Small Angular Velocity

The Kelvin–Helmholtz problem in a Hall plasma, including the effects of rotation, is studied. In contrast to previous results, it is shown that if the angular velocity is normal to the wave vector that describes perturbations of the interface, the rotation does not affect the stability of a shear plane. The special case of very small angular velocity is studied and it is shown that the rotation has either a stabilizing or a destabilizing effect, according as the gravitational speed is greater or less than the Alfvén speed.

On almost rigid rotations

1957 ◽  
Vol 3 (1) ◽  
pp. 17-26 ◽  
Author(s):  
K. Stewartson
Keyword(s):  
Boundary Layer ◽  
Angular Velocity ◽  
Shear Layer ◽  
The Other ◽  
Main Body ◽  
Rotating Fluids ◽  
Rotating Discs ◽  
Perturbation Velocity ◽  
Set Up ◽  
Small Angular Velocity

In order to answer some of Proudman's questions (1956) concerning shear layers in rotating fluids, a study is made of the flow between two coaxial rotating discs, each having an arbitrary small angular velocity superposed on a finite constant angular velocity. It is found that, if the perturbation velocity is a smooth function of r, the distance from the axis, then the angular velocity of the main body of fluid is determined by balancing the outflow from the boundary layer on one disc with the inflow to the boundary layer on the other at the same value of r. At a discontinuity in the angular velocity of either disc a shear layer parallel to the axis occurs. If the angular velocity of the main body of the fluid is continuous, according to the theory given below the purpose of this shear layer is solely to transfer fluid from the boundary layer on one disc to the boundary layer of the other. It has a thickness O(v1/3), where v is the kinematic viscosity, and in it the induced angular velocity is O(v1/6) of the perturbation angular velocity of the discs. On the other hand, if the angular velocity of the main body of fluid is discontinuous, according to the theory given below the thickness of the shear layer is O(v1/4). A secondary circulation is also set up in which fluid drifts parallel to the axis in this shear layer and is returned in an inner shear layer of thickness O(v1/3).The theory is also applied to the motion of fluid inside a closed circular cylinder of finite length rotating about its axis almost as if solid.

scholarly journals The Slow Spinning Motion of a Rigid Body in Newtonian Field and External Torque

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
A. I. Ismail
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
The Body ◽  
Slow Rotation ◽  
Large Parameter ◽  
Angular Velocity Vector ◽  
External Torque ◽  
Comparison Of The Results ◽  
Small Angular Velocity ◽  
Newtonian Force Field

In this paper, the problem of the slow spinning motion of a rigid body about a point O, being fixed in space, in the presence of the Newtonian force field and external torque is considered. We achieve the slow spin by giving the body slow rotation with a sufficiently small angular velocity component r 0 about the moving z-axis. We obtain the periodic solutions in a new domain of the angular velocity vector component r 0 ⟶ 0 , define a large parameter proportional to 1 / r 0 , and use the technique of the large parameter for solving this problem. Geometric interpretations of motions will be illustrated. Comparison of the results with the previous works is considered. A discussion of obtained solutions and results is presented.

Zonal and tesseral harmonic perturbations of an artificial satellite

1966 ◽  
Vol 25 ◽  
pp. 323-325 ◽  
Author(s):  
B. Garfinkel
Keyword(s):  
Angular Velocity ◽  
Spherical Harmonics ◽  
Artificial Satellite ◽  
Compact Form ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
Secular Variations ◽  
Tesseral Harmonics

The paper extends the known solution of the Main Problem to include the effects of the higher spherical harmonics of the geopotential. The von Zeipel method is used to calculate the secular variations of orderJmand the long-periodic variations of ordersJm/J2andnJm,λ/ω. HereJmandJm,λare the coefficients of the zonal and the tesseral harmonics respectively, withJm,0=Jm, andωis the angular velocity of the Earth's rotation. With the aid of the theory of spherical harmonics the results are expressed in a most compact form.

The Analysis of Proprioception Alteration during First Five Months after Anterior Cruciate Ligament Reconstruction

2018 ◽  
Vol 1 (84) ◽  
Author(s):  
Vilma Jurevičienė ◽  
Albertas Skurvydas ◽  
Juozas Belickas ◽  
Giedra Bušmanienė ◽  
Dovilė Kielė ◽  
...  
Keyword(s):  
Anterior Cruciate Ligament ◽  
Angular Velocity ◽  
Knee Joint ◽  
Cruciate Ligament ◽  
Position Sense ◽  
Joint Position Sense ◽  
Joint Position ◽  
Starting Position ◽  
Angular Velocities ◽  
Anterior Cruciate

Research  background  and  hypothesis.  Proprioception  is  important  in  the  prevention  of  injuries  as  reduced proprioception  is  one  of  the  factors  contributing  to  injury  in  the  knee  joint,  particularly  the  ACL.  Therefore, proprioception appears not only important for the prevention of ACL injuries, but also for regaining full function after ACL reconstruction.Research aim. The aim of this study was to understand how proprioception is recovered four and five months after anterior cruciate ligament (ACL) reconstruction.Research methods. The study included 15 male subjects (age – 33.7 ± 2.49 years) who had undergone unilateral ACL reconstruction with a semitendinosus/gracilis (STG) graft in Kaunas Clinical Hospital. For proprioceptive assessment, joint position sense (JPS) was measured on both legs using an isokinetic dynamometer (Biodex), at knee flexion of 60° and 70°, and at different knee angular velocities of 2°/s and 10°/s. The patients were assessed preoperatively and after 4 and 5 months, postoperatively.Research results. Our study has shown that the JPS’s (joint position sense) error scores  to a controlled active movement is significantly higher in injured ACL-deficient knee than in the contralateral knee (normal knee) before surgery and after four and five months of rehabilitation.  After 4 and 5 months of rehabilitation we found significantly lower values in injured knees compared to the preoperative data. Our study has shown that in injured knee active angle reproduction errors after 4 and 5 months of rehabilitation were higher compared with the ones of the uninjured knee. Proprioceptive ability on the both legs was  independent of all differences angles for target and starting position for movement. The knee joint position sense on both legs depends upon the rate of two different angular velocities and the mean active angle reproduction errors at the test of angular velocity slow speed was the highest compared with the fast angular velocity. Discussion and conclusions. In conclusion, our study shows that there was improvement in mean JPS 4 and 5 months after ACL reconstruction, but it did not return to normal indices.Keywords: knee joint, joint position sense, angular velocity, starting position for movement.

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