Resonance and chaos: II. Exterior resonances and asymmetric libration

The motion of a test particle in the vicinity of exterior resonances is examined in the context of the planar, circular, restricted three-body problem. The existence of asymmetric periodic orbits associated with the 1 : n resonances (where n = 2, 3, 4, 5) is confirmed; there is also evidence of asymmetric resonances associated with larger values of n. A detailed examination of the evolution of the family of orbits associated with the 1:2 resonance shows the sequence that leads to asymmetric libration. On the basis of numerical studies of the phase space it is concluded that the existence of asymmetric libration means that the region exterior to the perturbing mass is more chaotic than the interior region. The apparent absence of 'particles' in 1 : n resonances in the solar system may reflect this inherent bias.

Influence of Earth's shadow on the rotational motion of an artificial satellite perturbed by solar radiation torque

A semi-analytical approach is proposed to study the rotational motion of an artificial satellite under the influence of the torque due to the solar radiation pressure and taking into account the influence of Earth's shadow. The Earth's shadow is introduced in the equations for the rotational motion as a function depending on the longitude of the Sun, on the ecliptic's obliquity and on the orbital parameters of the satellite. By mapping and computing this function, we can get the periods in which the satellite is not illuminated and the torque due to the solar radiation pressure is zero. When the satellite is illuminated, a known analytical solution is used to predict the satellite's attitude. This analytical solution is expressed in terms of Andoyer's variables and depends on the physical and geometrical properties of the satellite and on the direction of the Sun radiation flux. By simulating a hypothetical circular cylindrical type satellite, an example is exhibited and the results agree quite well when compared with a numerical integration. © 1997 COSPAR. Published by Elsevier Science Ltd.

Carbon monoxide oxidation over platinum: Stable, oscillatory and quasi-chaotic regimes

We model the heterogeneously catalyzed oxidation of CO over a Pt surface. A phase diagram analysis is used to probe the several steady state regimes and their stability. We incorporate an experimentally observed 'slow' sub-oxide kinetic step, thereby generalizing a previously presented model. In agreement with experimental data, stable, oscillatory and quasi-chaotic regimes are obtained. Furthermore, the inclusion of the sub-oxide step yields a relaxation oscillation regime. © 1998 Elsevier Science B.V. All rights reserved.

Chaotic oscillation in an attractive Bose-Einstein condensate under an impulsive force

The chaotic oscillation in an attractive Bose-Einstein condensate (BEC) under an impulsive force was discussed using mean-field Gross-Pitaevskii (GP) equation. It was found that sustained chaotic oscillation resulted in a BEC under the action of an impulsive force generated by suddenly changing the interatomic scattering length or the harmonic oscillator trapping potential. The analysis suggested that the final state interatomic attraction played an important role in the generation of the chaotic dynamics.

Local dimension and finite time prediction in spatiotemporal chaotic systems

Predictability is related to the uncertainty in the outcome of future events during the evolution of the state of a system. The cluster weighted modeling (CWM) is interpreted as a tool to detect such an uncertainty and used it in spatially distributed systems. As such, the simple prediction algorithm in conjunction with the CWM forms a powerful set of methods to relate predictability and dimension.

A contribution for nonlinear structural dynamics characterization of cantilever beams

Successful experiments in nonlinear vibrations have been carried out with cantilever beams under harmonic base excitation. A flexible slender cantilever has been chosen as a convenient structure to exhibit modal interactions, subharmonic, superharmonic and chaotic motions, and others interesting nonlinear phenomena. The tools employed to analyze the dynamics of the beam generally include frequency- and force-response curves. To produce force-response curves, one keeps the excitation frequency constant and slowly varies the excitation amplitude, on the other hand, to produce frequency-response curves, one keeps the excitation amplitude fixed and slowly varies the excitation frequency. However, keeping the excitation amplitude constant while varying the excitation frequency is a difficult task with an open-loop measurement system. In this paper, it is proposed a closed-loop monitor vibration system available with the electromagnetic shaker in order to keep the harmonic base excitation amplitude constant. This experimental setup constitutes a significant improvement to produce frequency-response curves and the advantages of this setup are evaluated in a case study. The beam is excited with a periodic base motion transverse to the axis of the beam near the third natural frequency. Modal interactions and two-period quasi-periodic motion are observed involving the first and the third modes. Frequency-response curves, phase space and Poincaré map are used to characterize the dynamics of the beam.

Optimal linear and nonlinear control design for chaotic systems

In this work, the linear and nonlinear feedback control techniques for chaotic systems were been considered. The optimal nonlinear control design problem has been resolved by using Dynamic Programming that reduced this problem to a solution of the Hamilton-Jacobi-Bellman equation. In present work the linear feedback control problem has been reformulated under optimal control theory viewpoint. The formulated Theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations for the Rössler system and the Duffing oscillator are provided to show the effectiveness of this method. Copyright © 2005 by ASME.

Influence of nonsphericity of planetary satellites and perturbation of the third-body on the artificial satellites motion

Some orbital characteristics of lunar artificial satellites is presented taking into account the perturbation of the third-body in elliptical orbit and the non-uniform distribution of mass of the Moon. We consider the development of the non-sphericity of the Moon in zonal spherical harmonics up to the ninth order and sectorial harmonic C 22 due to the lunar equatorial ellipticity. The motion of the artificial satellite is studied under the single-averaged analytical model. The average is applied to the mean anomaly of the satellite to analyze low-altitude orbits which are of highest importance for future lunar missions. We found families of frozen orbits with long lifetimes for the problem of an orbiter travelling around the Moon.

Maximal isokinetic peak torque and EMG activity determined by shorter ranges of motion

Purpose. Isokinetic tests are often applied to assess muscular strength and EMG activity, however the specific ranges of motion used in testing (fully flexed or extended positions) might be constrictive and/or be painful for patients with injuries or under-going rehabilitation. The aim of this study was to examine the effects of different ranges of motion (RoM) when determining maximal EMG during isokinetic knee flexion and extension with different types of contractions and velocities. Methods. Eighteen males had EMG activity recorded on the vastus lateralis, vastus medialis, semitendinosus and biceps femoris muscles during five maximal isokinetic concentric and eccentric contractions for the knee flexors and extensors at 60° • s -1 and 180° • s -1. The root mean square of EMG was calculated at three different ranges of motion: (1) a full range of motion (90°-20° [0° = full knee extension]); (2) a range of motion of 20° (between 60°-80° and 40°-60° for knee extension and flexion, respectively) and (3) at a 10° interval around the angle where peak torque is produced. EMG measurements were statistically analyzed (ANOVA) to test for the range of motion, contraction velocity and contraction speed effects. Coefficients of variation and Pearson's correlation coefficients were also calculated among the ranges of motion. Results. Predominantly similar (p > 0.05) and well-correlated EMG results (r > 0.7, p ≤ 0.001) were found among the ranges of motion. However, a lower coefficient of variation was found for the full range of motion, while the 10° interval around peak torque at 180° • s -1 had the highest coefficient, regardless of the type of contraction. Conclusions. Shorter ranges of motion at around the peak torque angle provides a reliable indicator when recording EMG activity during maximal isokinetic parameters. It may provide a safer alternative when testing patients with injuries or undergoing rehabilitation.

Analytical direct planetary perturbations on the orbital motion of satellites

An analytical expansion of the disturbing function arising from direct planetary perturbations on the motion of satellites is derived. As a Fourier series, it allows the investigation of the secular effects of these direct perturbations, as well as of every argument present in the perturbation. In particular, we construct an analytical model describing the evection resonance between the longitude of pericenter of the satellite orbit and the longitude of a planet, and study briefly its dynamic. The expansion developed in this paper is valid in the case of planar and circular planetary orbits, but not limited in eccentricity or inclination of the satellite orbit. © 2012 Springer Science+Business Media Dordrecht.

On Non-ideal and Chaotic Energy Harvester Behavior

In this paper, we deal with the research of a proposed mathematical model of energy harvesting, including nonlinearities in the piezoelectric coupling and a non-ideal force of excitation. We showed using numerical simulations to analysis of the dynamic responses that, the power harvested was influenced by the nonlinear vibrations of the structure, as well as by the influence of the non-linearities in the piezoelectric coupling. We concluded through of the numerical results that the limited energy source was interacting with the system. Thus, the increasing of the voltage in DC motor led the system produce a good power response, especially in high-energy orbits in the resonance region, but the Sommerfeld effect occurs in the system and a chaotic behavior was found in the post-resonance region. So the power harvested along the time decreases because occurs loses of energy due the interaction between energy source and structure. Keeping the energy harvested constant over time is essential to make possible the use of energy harvesting systems in real applications. To achieve this objective, we applied a control technique in order to stabilize the chaotic system in a periodic stable orbit. We announced that the results were satisfactory and the control maintained the system in a stable condition. © 2012 Foundation for Scientific Research and Technological Innovation.

On the Chaotic Suppression of Both Ideal and Non-ideal Duffing Based Vibrating Systems, Using a Magnetorheological Damper

In this paper the dynamics of the ideal and non-ideal Duffing oscillator with chaotic behavior is considered. In order to suppress the chaotic behavior and to control the system, a control signal is introduced in the system dynamics. The control strategy involves the application of two control signals, a nonlinear feedforward control to maintain the controlled system in a periodic orbit, obtained by the harmonic balance method, and a state feedback control, obtained by the state dependent Riccati equation, to bring the system trajectory into the desired periodic orbit. Additionally, the control strategy includes an active magnetorheological damper to actuate on the system. The control force of the damper is a function of the electric current applied in the coil of the damper, that is based on the force given by the controller and on the velocity of the damper piston displacement. Numerical simulations demonstrate the effectiveness of the control strategy in leading the system from any initial condition to a desired orbit, and considering the mathematical model of the damper (MR), it was possible to control the force of the shock absorber (MR), by controlling the applied electric current in the coils of the damper. © 2012 Foundation for Scientific Research and Technological Innovation.

Chaotic diffusion caused by close encounters with several massive asteroids: II. the regions of (10) Hygiea, (2) Pallas, and (31) Euphrosyne

Context. Close encounters with (1) Ceres and (4) Vesta, the two most massive bodies in the main belt, are known to be a mechanism of dynamical mobility able to significantly alter proper elements of minor bodies, and they are the main source of dynamical mobility for medium-sized and large asteroids (D > 20 km, approximately). Recently, it has been shown that drift rates caused by close encounters with massive asteroids may change significantly on timescales of 30 Myr when different models (i.e., different numbers of massive asteroids) are considered. Aims. So far, not much attention has been given to the case of diffusion caused by the other most massive bodies in the main belt: (2) Pallas, (10) Hygiea, and (31) Euphrosyne, the third, fourth, and one of the most massive highly inclined asteroids in the main belt, respectively. Since (2) Pallas is a highly inclined object, relative velocities at encounter with other asteroids tend to be high and changes in proper elements are therefore relatively small. It was thus believed that the scattering effect caused by highly inclined objects in general should be small. Can diffusion by close encounters with these asteroids be a significant mechanism of long-term dynamical mobility? Methods. By performing simulations with symplectic integrators, we studied the problem of scattering caused by close encounters with (2) Pallas, (10) Hygiea, and (31) Euphrosyne when only the massive asteroids (and the eight planets) are considered, and the other massive main belt asteroids and non-gravitational forces are also accounted for. Results. By finding relatively small values of drift rates for (2) Pallas, we confirm that orbital scattering by this highly inclined object is indeed a minor effect. Unexpectedly, however, we obtained values of drift rates for changes in proper semi-major axis a caused by (10) Hygiea and (31) Euphrosyne larger than what was previously found for scattering by (4) Vesta. These high rates may have repercussions on the orbital evolution and age estimate of their respective families. © 2013 ESO.

Effect of Storage Time and Temperature of Equine Epididymis on the Viability, Motion Parameters, and Freezability of Epididymal Sperm

The recovery of sperm from the epididymal cauda may be the last chance to obtain genetic material when sudden death or serious injuries occur in valuable stallions. However, the lack of technical knowledge regarding the storage and transportation of the epididymis often prevents the preservation of the sperm. Therefore, the aim of this study was to compare sperm parameters of sperm obtained immediately after orchiectomy with sperm recovered from epididymal cauda at different times after storage at 5°C and at room temperature (RT). For that, 48 stallions of different breeds were used. In group 1 (control group), eight stallions were used, and the harvest of the epididymal sperm was performed immediately after orchiectomy. In group 2, 40 stallions were used, which were divided into five groups according to the storage time of the epididymis after orchiectomy (6, 12, 18, 24, or 30 hours), making a total of eight stallions per group. One epididymis of each stallion was stored at 5°C, and the contralateral epididymis was stored at RT, both for the same period. The sperm parameters of total motility, progressive motility, progressive linear velocity, curvilinear velocity, percentage of rapid sperm, and plasma membrane integrity were evaluated in all the groups after sperm recovery, resuspension in a sperm freezing diluent, and thawing. In conclusion, the storage of the testis-epididymis complex at 5°C provided better preservation of epididymal sperm than the storage at RT, and regardless of the temperature, the progressive motility is the sperm parameter that is most sensitive to storage time. © 2013 Elsevier Inc.

Coordination of spinal motion in the transverse and frontal planes during walking in people with and without recurrent low back pain

STUDY DESIGN. Observational cohort study. OBJECTIVE. To investigate spinal coordination during preferred and fast speed walking in pain-free subjects with and without a history of recurrent low back pain (LBP). SUMMARY OF BACKGROUND DATA. Dynamic motion of the spine during walking is compromised in the presence of back pain (LBP), but its analysis often presents some challenges. The coexistence of significant symptoms may change gait because of pain or adaptation of the musculoskeletal structures or both. A history of LBP without the overlay of a current symptomatic episode allows a better model in which to explore the impact on spinal coordination during walking. METHODS. Spinal and lower limb segmental motions were tracked using electromagnetic sensors. Analyses were conducted to explore the synchrony and spatial coordination of the segments and to compare the control and subjects with LBP. RESULTS. We found no apparent differences between the groups for either overall amplitude of motion or most indicators of coordination in the lumbar region; however, there were significant postural differences in the mid-stance phase and other indicators of less phase locking in controls compared with subjects with LBP. The lower thoracic spinal segment was more affected by the history of back pain than the lumbar segment. CONCLUSION. Although small, there were indicators that alterations in spinal movement and coordination in subjects with recurrent LBP were due to adaptive changes rather than the presence of pain. © 2013, Lippincott Williams & Wilkins.