The onset of chaotic motion in the restricted problem of three bodies

1993 ◽  
Vol 56 (3) ◽  
pp. 409-425 ◽  
Author(s):  
R. H. Smith ◽  
V. Szebehely
Keyword(s):  
Chaotic Motion ◽  
Restricted Problem

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

On nearly-commensurable periods in the restricted problem of three bodies, with calculations of the long-period variations in the interior 2:1 case

1966 ◽  
Vol 25 ◽  
pp. 197-222 ◽  
Author(s):  
P. J. Message
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Large Amplitude ◽  
Restricted Problem ◽  
Small Amplitude ◽  
Minor Planets ◽  
Long Period ◽  
Numerical Integrations ◽  
Period Variations ◽  
The Mean

An analytical discussion of that case of motion in the restricted problem, in which the mean motions of the infinitesimal, and smaller-massed, bodies about the larger one are nearly in the ratio of two small integers displays the existence of a series of periodic solutions which, for commensurabilities of the typep+ 1:p, includes solutions of Poincaré'sdeuxième sortewhen the commensurability is very close, and of thepremière sortewhen it is less close. A linear treatment of the long-period variations of the elements, valid for motions in which the elements remain close to a particular periodic solution of this type, shows the continuity of near-commensurable motion with other motion, and some of the properties of long-period librations of small amplitude.To extend the investigation to other types of motion near commensurability, numerical integrations of the equations for the long-period variations of the elements were carried out for the 2:1 interior case (of which the planet 108 “Hecuba” is an example) to survey those motions in which the eccentricity takes values less than 0·1. An investigation of the effect of the large amplitude perturbations near commensurability on a distribution of minor planets, which is originally uniform over mean motion, shows a “draining off” effect from the vicinity of exact commensurability of a magnitude large enough to account for the observed gap in the distribution at the 2:1 commensurability.

Quantum Computing and the Onset of Quantum Chaotic Motion

2002 ◽  
Author(s):  
Giulio Casati ◽  
Carlo Beenakker ◽  
Tomaz Prozen ◽  
Philippe Jacquod ◽  
Giuliano Benenti
Keyword(s):  
Quantum Computing ◽  
Chaotic Motion

New results on the possible chaotic motion of Enceladus

1987 ◽  
Vol 43 (1-4) ◽  
pp. 361-369 ◽  
Author(s):  
M. Karch ◽  
R. Dvorak
Keyword(s):  
Chaotic Motion

A Simple Model for the Chaotic Motion Around (433) Eros

2003 ◽  
Vol 51 (4) ◽  
pp. 391-404 ◽  
Author(s):  
Antonio Elipe ◽  
Martín Lara
Keyword(s):  
Simple Model ◽  
Chaotic Motion

scholarly journals Accurate predictions of chaotic motion of a free fall disk

2021 ◽  
Vol 33 (3) ◽  
pp. 037111
Author(s):  
Tianzhuang Xu ◽  
Jing Li ◽  
Zhihui Li ◽  
Shijun Liao
Keyword(s):  
Chaotic Motion ◽  
Free Fall

Multi-Stable Magnetic Spring-Based Energy Harvester Subject to Harmonic Excitation: Comparative Study and Experimental Evaluation

2018 ◽  
Author(s):  
Hieu Nguyen ◽  
Hamzeh Bardaweel
Keyword(s):  
Energy Harvesting ◽  
Kinetic Energy ◽  
Comparative Study ◽  
Experimental Evaluation ◽  
Chaotic Motion ◽  
Energy Harvester ◽  
Electric Energy ◽  
Harmonic Excitation ◽  
Jump Frequency ◽  
Piezoelectric Elements

The work presented here investigates a unique design platform for multi-stable energy harvesting using only interaction between magnets. A solid cylindrical magnet is levitated between two stationary magnets. Peripheral magnets are positioned around the casing of the energy harvester to create multiple stable positions. Upon external vibration, kinetic energy is converted into electric energy that is extracted using a coil wrapped around the casing of the harvester. A prototype of the multi-stable energy harvester is fabricated. Monostable and bistable configurations are demonstrated and fully characterized in static and dynamic modes. Compared to traditional multi-stable designs the harvester introduced in this work is compact, occupies less volume, and does not require complex circuitry normally needed for multi-stable harvesters involving piezoelectric elements. At 2.5g [m/s2], results from experiment show that the bistable harvester does not outperform the monostable harvester. At this level of acceleration, the bistable harvester exhibits intrawell motion away from jump frequency. Chaotic motion is observed in the bistable harvester when excited close to jump frequency. Interwell motion that yields high displacement amplitudes and velocities is absent at this acceleration.

Chaotic motion of magnetotactic bacteria

2000 ◽  
Vol 11 (6) ◽  
pp. 923-928 ◽  
Author(s):  
P.H.A. Aragão ◽  
M. Simões
Keyword(s):  
Chaotic Motion ◽  
Magnetotactic Bacteria
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