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.

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.

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.

Instability and Chaos in Quadruped Gallop

1994 ◽  
Vol 116 (4) ◽  
pp. 1096-1101 ◽  
Author(s):  
P. Nanua ◽  
K. J. Waldron
Keyword(s):  
Chaotic Behavior ◽  
Initial Conditions ◽  
The Body ◽  
Main Body ◽  
Viscous Damper ◽  
System Parameters ◽  
Constant Stiffness ◽  
Speed Controller ◽  
Symmetry Principles ◽  
The Stability

A dynamic model for the two-dimensional quadruped has been developed. The main body is modelled as a rigid bar and each leg consists of a constant stiffness spring, a viscous damper and a force actuator. Based on symmetry principles, a controller has been devised that will enable the quadruped to gallop at constant speed. The controller consists of two parts: an energy controller which will apply the required amount of force through the legs, and the speed controller that will control the forward speed by appropriately placing the legs. It will be shown that the body pitch need not be explicitly controlled. The stability of this controller will be examined using Poincare maps. Stable systems show either periodic or quasi-periodic response. This system also exhibits chaotic behavior and chaotic response results in instability. The stability of the system with changes in the initial conditions, as well as variations in the system parameters, will also be examined. It will be shown that the system is stable for a range of leg stiffnesses. Outside this range, the system shows chaotic behavior.

Research on Automobile Aerodynamic Drag Reduction Based on Isobaric Surface of a Blunt Body

2013 ◽  
Vol 328 ◽  
pp. 634-638
Author(s):  
Xing Jun Hu ◽  
Lei Liao ◽  
Xiu Cheng Li ◽  
Chang Hai Yang ◽  
Peng Guo ◽  
...  
Keyword(s):  
Drag Reduction ◽  
Blunt Body ◽  
Aerodynamic Drag ◽  
Simulation Method ◽  
The Body ◽  
Viscous Drag ◽  
Isobaric Surface ◽  
Pressure Drag ◽  
Aerodynamic Drag Reduction ◽  
The Relationship

This paper focuses on a new method of aerodynamic drag reduction. In this paper numerical simulation method is adopted to investigate the relationship between the aerodynamic drag characteristics of a blunt body and the distribution of total pressure around the body. The study shows that when the shape of a blunt body is modified to be close to its isobaric surface, the pressure drag of the body can be reduced largely while the viscous drag increases slightly, and the summary of the drag gets lower as a result. This conclusion will have profound guiding significance in the aerodynamic shape designing and the aerodynamic drag reduction of an automobile.

CHAOTIC PITCH MOTION OF A MAGNETIC SPACECRAFT WITH VISCOUS DRAG IN AN ELLIPTICAL POLAR ORBIT

2011 ◽  
Vol 21 (07) ◽  
pp. 1959-1975 ◽  
Author(s):  
MANUEL IÑARREA
Keyword(s):  
Chaotic Behavior ◽  
Melnikov Method ◽  
Numerical Continuation ◽  
Viscous Drag ◽  
Gravity Gradient ◽  
Attitude Dynamics ◽  
Small Eccentricity ◽  
Pitch Motion ◽  
Analytical Criterion ◽  
Perturbation Parameters

We study the pitch attitude dynamics of an asymmetric magnetic spacecraft in an almost circular orbit under the influence of a gravity gradient torque. The spacecraft is also subject to the influence of three perturbations: the small eccentricity of the elliptical orbit, a small magnetic torque due to the interaction with the Earth's magnetic field, and a small aerodynamic viscous drag generated by the action of the Earth's atmosphere. Under these perturbations, we show that the pitch motion exhibits heteroclinic chaotic behavior by means of the Melnikov method. This method gives us an analytical criterion for the existence of heteroclinic chaos in terms of the system parameters. This analytical criterion is confirmed numerically with good agreement. In spite of the chaos generated by the perturbations, we also find, by means of Poincaré surfaces of section that some periodic pitch motions persist in the perturbed system with the same period as the orbital motion of the spacecraft. Finally, we carry out a bifurcation analysis of these periodic motions by numerical continuation of them in terms of the perturbation parameters.

Instability and Chaos in Quadruped Gallop

1992 ◽  
Author(s):  
Prabjot Nanua ◽  
Kenneth J. Waldron
Keyword(s):  
Chaotic Behavior ◽  
Initial Conditions ◽  
The Body ◽  
Main Body ◽  
Viscous Damper ◽  
System Parameters ◽  
Constant Stiffness ◽  
Speed Controller ◽  
Symmetry Principles ◽  
The Stability

Abstract A dynamic model for the two dimensional quadruped has been developed. The main body is modelled as a rigid bar and each leg consists of a constant stiffness spring, a viscous damper and a force actuator. Based on symmetry principles, a controller has been devised that will enable the quadruped to gallop at constant speed. The controller consists of two parts: an energy controller which will apply the required amount of force through the legs, and the speed controller that will control the forward speed by appropriately placing the legs. It will be shown that the body pitch need not be explicitly controlled. The stability of this controller will be examined using Poincare maps. Stable systems show either periodic or quasi-periodic response. This system also exhibits chaotic behavior and chaotic response leads to instability. The stability of the system with changes in the initial conditions, as well as variations in the system parameters, will also be examined. It will be shown that the system is stable for a range of leg stiffnesses. Outside this range, the system shows chaotic behavior.

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.

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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