Spin Rotor Stabilization of a Dual-Spin Spacecraft with Time Dependent Moments of Inertia

1998 ◽  
Vol 08 (03) ◽  
pp. 609-617 ◽  
Author(s):  
V. Lanchares ◽  
M. Iñarrea ◽  
J. P. Salas
Keyword(s):  
Periodic Function ◽  
Center Of Mass ◽  
The Body ◽  
Body Motion ◽  
Time Dependent ◽  
Moments Of Inertia ◽  
Melnikov's Method ◽  
Melnikov’S Method ◽  
Principal Axes

We consider a dual-spin deformable spacecraft, in the sense that one of the moments of inertia is a periodic function of time such that the center of mass is not altered. In the absence of external torques and spin rotors, by means of the Melnikov's method we prove that the body motion is chaotic. Stabilization is obtained by means of a spinning rotor about one of the principal axes of inertia.

CHAOTIC ROTATIONS OF AN ASYMMETRIC BODY WITH TIME-DEPENDENT MOMENTS OF INERTIA AND VISCOUS DRAG

2003 ◽  
Vol 13 (02) ◽  
pp. 393-409 ◽  
Author(s):  
M. IÑARREA ◽  
V. LANCHARES ◽  
V. M. ROTHOS ◽  
J. P. SALAS
Keyword(s):  
Aerodynamic Drag ◽  
Chaotic Behavior ◽  
Center Of Mass ◽  
The Body ◽  
Time Dependent ◽  
Viscous Drag ◽  
Moments Of Inertia ◽  
System Parameters ◽  
Higher Dimensional ◽  
Analytical Criterion

We study the dynamics of a rotating asymmetric body under the influence of an aerodynamic drag. We assume that the drag torque is proportional to the angular velocity of the body. Also we suppose that one of the moments of inertia of the body is a periodic function of time and that the center of mass of the body is not modified. Under these assumptions, we show that the system exhibits a transient chaotic behavior by means of a higher dimensional generalization of the Melnikov's method. This method give us an analytical criterion for heteroclinic chaos in terms of the system parameters. These analytical results are confirmed by computer numerical simulations of the system rotations.

CHAOS IN THE REORIENTATION PROCESS OF A DUAL-SPIN SPACECRAFT WITH TIME-DEPENDENT MOMENTS OF INERTIA

2000 ◽  
Vol 10 (05) ◽  
pp. 997-1018 ◽  
Author(s):  
M. IÑARREA ◽  
V. LANCHARES
Keyword(s):  
Chaotic Behavior ◽  
Initial Conditions ◽  
Center Of Mass ◽  
Melnikov Method ◽  
Moments Of Inertia ◽  
Suitable Parameter ◽  
Nutation Angle ◽  
Principal Axes ◽  
Reorientation Process ◽  
Subharmonic Resonances

We study the spin-up dynamics of a dual-spin spacecraft containing one axisymmetric rotor which is parallel to one of the principal axes of the spacecraft. It will be supposed that one of the moments of inertia of the platform is a periodic function of time and that the center of mass of the spacecraft is not modified. Under these assumptions, it is shown that in the absence of external torques and spinning rotors the system possesses chaotic behavior in the sense that it exhibits Smale's horseshoes. We prove this statement by means of the Melnikov method. The presence of chaotic behavior results in a random spin-up operation. This randomness is visualized by means of maps of the initial conditions with final nutation angle close to zero. This phenomenon is well described by a suitable parameter that measures the amount of randomness of the process. Finally, we relate this parameter with the Melnikov function in the absence of the spinning rotor and with the presence of subharmonic resonances.

scholarly journals Stability of rigid body motion through an extended intermediate axis theorem: application to rockfall simulation

2021 ◽  
Author(s):  
Remco I. Leine ◽  
Giuseppe Capobianco ◽  
Perry Bartelt ◽  
Marc Christen ◽  
Andrin Caviezel
Keyword(s):  
Rigid Body ◽  
Direct Method ◽  
Lateral Spreading ◽  
The Body ◽  
Body Motion ◽  
Numerical Schemes ◽  
Stability Properties ◽  
Principal Axes ◽  
Rockfall Simulation ◽  
The Stability

AbstractThe stability properties of a freely rotating rigid body are governed by the intermediate axis theorem, i.e., rotation around the major and minor principal axes is stable whereas rotation around the intermediate axis is unstable. The stability of the principal axes is of importance for the prediction of rockfall. Current numerical schemes for 3D rockfall simulation, however, are not able to correctly represent these stability properties. In this paper an extended intermediate axis theorem is presented, which not only involves the angular momentum equations but also the orientation of the body, and we prove the theorem using Lyapunov’s direct method. Based on the stability proof, we present a novel scheme which respects the stability properties of a freely rotating body and which can be incorporated in numerical schemes for the simulation of rigid bodies with frictional unilateral constraints. In particular, we show how this scheme is incorporated in an existing 3D rockfall simulation code. Simulations results reveal that the stability properties of rotating rocks play an essential role in the run-out length and lateral spreading of rocks.

scholarly journals On the dynamical motion of a gyro in the presence of external forces

2017 ◽  
Vol 9 (2) ◽  
pp. 168781401769173 ◽  
Author(s):  
T. S. Amer
Keyword(s):  
Force Field ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
The Body ◽  
Parameter Method ◽  
Newtonian Force ◽  
Principal Axes ◽  
External Forces ◽  
Newtonian Force Field

This work shed light on the motion of a symmetric rigid body (gyro) about one of its principal axes in the presence of a Newtonian force field besides a gyro moment in which its second component equals null. It is assumed that the body center of mass is shifted slightly relative to the dynamic symmetry axis. The governing equations of motion are investigated taking into account some initial conditions. The desired solutions of these equations are achieved in framework of the small parameter method. The periodic solutions for the case of irrational frequencies are investigated. Euler’s angles have been used to interpret the motion at any time. The geometrical representations of the obtained solutions and the phase plane schemas of these solutions are announced during several plots. Discussion of the results is presented to reinforce the importance of the considered gyro moment and the Newtonian force field. The significance of this problem is due to the framework of its several applications in different industries such as airplanes, submarines, compasses, spaceships, and guided missiles.

A Theoretical and Numerical Study of the Dzhanibekov and Tennis Racket Phenomena

2015 ◽  
Author(s):  
Hidenori Murakami ◽  
Oscar Rios ◽  
Thomas J. Impelluso
Keyword(s):  
Numerical Study ◽  
Space Station ◽  
The Body ◽  
Moving Frame ◽  
Coordinate Frame ◽  
Moments Of Inertia ◽  
Tennis Racket ◽  
Angular Momenta ◽  
Principal Axes ◽  
Moving Coordinate

In this paper, we present complete explanation of the Dzhanibekov phenomenon demonstrated in a space station (www.youtube.com/watch?v=L2o9eBl_Gzw) and the tennis racket phenomenon (www.youtube.com/watch?v=4dqCQqI-Gis). These phenomena are described by Euler’s equation of an unconstrained rigid body that has three distinct values of moments of inertia. In the two phenomena, the rotations of a body about the principal axes that correspond to the largest and the smallest moments of inertia are stable. However, the rotation about the axis corresponding to the intermediate principal moment of inertia becomes unstable, leading to the unexpected rotations that are the basis of the phenomena. If this unexpected rotation is not explained from a complete perspective which accounts for the relevant physical and mathematical aspects, one might misconstrue the phenomena as a violation of the conservation of angular momenta. To address this, especially for students, we investigate the phenomena using more precise mathematical and graphical tools than those employed previously. Following Élie Cartan [1], we explicitly write the vector basis of a body-attached, moving coordinate system. Using this moving frame method, we describe the Newton and Euler equations. The adoption of the moving coordinate frame expresses the rotation of the body more clearly and allows us to use the Lie group theory of special orthogonal group SO(3). We integrate the torque-free Euler equation using the fourth-order Runge-Kutta method. Then we apply a recovery equation to obtain the rotation matrix for the body. By combining the geometrical solutions with numerical simulations, we demonstrate that the unexpected rotations observed in the Dzhanibekov and the tennis racket experiments preserve the conservation of angular momentum.

scholarly journals Vestibular modulation of visuomotor feedback gains in reaching

2019 ◽  
Vol 122 (3) ◽  
pp. 947-957 ◽  
Author(s):  
Leonie Oostwoud Wijdenes ◽  
Robert J. van Beers ◽  
W. Pieter Medendorp
Keyword(s):  
Feedback Control ◽  
The Body ◽  
Body Motion ◽  
Time Dependent ◽  
Reaching Movements ◽  
Optimal Feedback Control ◽  
Optimal Feedback ◽  
Vestibular Information ◽  
The World ◽  
Full Body

Humans quickly and sophisticatedly correct their movements in response to changes in the world, such as when reaching to a target that abruptly changes its location. The vigor of these movement corrections is time-dependent, increasing if the time left to make the correction decreases, which can be explained by optimal feedback control (OFC) theory as an increase of optimal feedback gains. It is unknown whether corrections for changes in the world are as sophisticated under full-body motion. For successful visually probed motor corrections during full-body motion, not only the motion of the hand relative to the body needs to be taken into account, but also the motion of the hand in the world should be considered, because their relative positions are changing. Here, in two experiments, we show that visuomotor feedback corrections in response to target jumps are more vigorous for faster passive full-body translational acceleration than for slower acceleration, suggesting that vestibular information modulates visuomotor feedback gains. Interestingly, these corrections do not demonstrate the time-dependent characteristics that body-stationary visuomotor feedback gains typically show, such that an optimal feedback control model fell short to explain them. We further show that the vigor of corrections generally decreased over the course of trials within the experiment, suggesting that the sensorimotor system adjusted its gains when learning to integrate the vestibular input into hand motor control. NEW & NOTEWORTHY Vestibular information is used in the control of reaching movements to world-stationary visual targets, while the body moves. Here, we show that vestibular information also modulates the corrective reach responses when the target changes position during the body motion: visuomotor feedback gains increase for faster body acceleration. Our results suggest that vestibular information is integrated into fast visuomotor control of reaching movements.

scholarly journals The Stability Conditions for a Heavy Solid Motion

2020 ◽  
Vol 2020 ◽  
pp. 1-4
Author(s):  
A. I. Ismail
Keyword(s):  
Equations Of Motion ◽  
Center Of Mass ◽  
Sufficient Conditions ◽  
The Body ◽  
Stability Conditions ◽  
Moments Of Inertia ◽  
Principal Moments Of Inertia ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
Necessary And Sufficient

In this paper, the stability conditions for the rotary motion of a heavy solid about its fixed point are considered. The center of mass of the body is assumed to lie on the moving z-axis which is assumed to be the minor axis of the ellipsoid of inertia. The nonlinear equations of motion and their three first integrals are obtained when the principal moments of inertia are distributed as I 1 < I 2 < I 3 . We construct a Lyapunov function L to investigate the stability conditions for this motion. We give a numerical example to illustrate the necessary and sufficient conditions for the stability of the body at certain moments of inertia. This problem has many important applications in different sciences.

On the motion of bodies based on changes in the kinetic moment

2019 ◽  
Vol 20 (4) ◽  
pp. 267-275
Author(s):  
Yury N. Razoumny ◽  
Sergei A. Kupreev
Keyword(s):  
Center Of Mass ◽  
Stellar Dynamics ◽  
Elementary Particles ◽  
The Body ◽  
Accelerated Motion ◽  
Indirect Confirmation ◽  
Physical Principles ◽  
Two Bodies ◽  
Central Gravitational Field ◽  
Kinetic Moment

The controlled motion of a body in a central gravitational field without mass flow is considered. The possibility of moving the body in the radial direction from the center of attraction due to changes in the kinetic moment relative to the center of mass of the body is shown. A scheme for moving the body using a system of flywheels located in the same plane in near-circular orbits with different heights is proposed. The use of the spin of elementary particles is considered as flywheels. It is proved that using the spin of elementary particles with a Compton wavelength exceeding the distance to the attracting center is energetically more profitable than using the momentum of these particles to move the body. The calculation of motion using hypothetical particles (gravitons) is presented. A hypothesis has been put forward about the radiation of bodies during accelerated motion, which finds indirect confirmation in stellar dynamics and in an experiment with the fall of two bodies in a vacuum. The results can be used in experiments to search for elementary particles with low energy, explain cosmic phenomena and to develop transport objects on new physical principles.

Chaos in body–vortex interactions

2010 ◽  
Vol 466 (2119) ◽  
pp. 1871-1891 ◽  
Author(s):  
Johan Roenby ◽  
Hassan Aref
Keyword(s):  
Body Shape ◽  
Mass Density ◽  
Relative Equilibrium ◽  
Large Body ◽  
Point Vortex ◽  
Cylindrical Body ◽  
The Body ◽  
Body Motion ◽  
Single Vortex ◽  
Vortex Interactions

The model of body–vortex interactions, where the fluid flow is planar, ideal and unbounded, and the vortex is a point vortex, is studied. The body may have a constant circulation around it. The governing equations for the general case of a freely moving body of arbitrary shape and mass density and an arbitrary number of point vortices are presented. The case of a body and a single vortex is then investigated numerically in detail. In this paper, the body is a homogeneous, elliptical cylinder. For large body–vortex separations, the system behaves much like a vortex pair regardless of body shape. The case of a circle is integrable. As the body is made slightly elliptic, a chaotic region grows from an unstable relative equilibrium of the circle-vortex case. The case of a cylindrical body of any shape moving in fluid otherwise at rest is also integrable. A second transition to chaos arises from the limit between rocking and tumbling motion of the body known in this case. In both instances, the chaos may be detected both in the body motion and in the vortex motion. The effect of increasing body mass at a fixed body shape is to damp the chaos.

scholarly journals Detection of Acetaminophen and Its Glucuronide in Fingerprint by SALDI Mass Spectrometry Using Zeolite and Study of Time-Dependent Changes in Detected Ion Amount

Analytica ◽  
2021 ◽  
Vol 2 (3) ◽  
pp. 66-75
Author(s):  
Toshiki Horikoshi ◽  
Chihiro Kitaoka ◽  
Yosuke Fujii ◽  
Takashi Asano ◽  
Jiawei Xu ◽  
...  
Keyword(s):  
Mass Spectrometry ◽  
Glucuronic Acid ◽  
Laser Desorption ◽  
The Body ◽  
Time Dependent ◽  
Laser Desorption Ionization ◽  
Fingerprint Analysis ◽  
Desorption Ionization ◽  
Acid Conjugate ◽  
Over Time

The ingredients of an antipyretic (acetaminophen, AAP) and their metabolites excreted into fingerprint were detected by surface-assisted laser desorption ionization (SALDI) mass spectrometry using zeolite. In the fingerprint taken 4 h after AAP ingestion, not only AAP but also the glucuronic acid conjugate of AAP (GAAP), caffeine (Caf), ethenzamide (Eth), salicylamide (Sala; a metabolite of Eth), and urea were detected. Fingerprints were collected over time to determine how the amounts of AAP and its metabolite changed with time, and the time dependence of the peak intensities of protonated AAP and GAAP was measured. It was found that the increase of [GAAP+H]+ peak started later than that of [AAP+H]+ peak, reflecting the metabolism of AAP. Both AAP and GAAP reached maximum concentrations approximately 3 h after ingestion, and were excreted from the body with a half-life of approximately 3.3 h. In addition, fingerprint preservation was confirmed by optical microscopy, and fingerprint shape was retained even after laser irradiation of the fingerprint. Our method may be used in fingerprint analysis.

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