Stable Orbit Research Articles

TLS Fast Orbit Feedback Upgrade

The Orbit Feedback System (OFB) at the Taiwan Light Source (TLS) was implemented two decades ago and has undergone multiple upgrades to enhance its performance. The loop bandwidth was constrained by the available hardware. The system is unable to eliminate perturbations from a fast source. In order to enhance the performance of orbit feedback, the system underwent an upgrade in 2008. The upgrade involved the replacement of the analog-type BPM electronics with digital BPM electronics, as well as the replacement of the corrector power supply with a high-performance switching-type power supply that has a wide bandwidth. Following the commissioning of the Taiwan Photon Source (TPS) in 2015, a decision was made to gradually migrate the control system of the Taiwan Light Source to the Experimental Physics and Industrial Control System (EPICS). This decision was made in order to facilitate resource sharing between the two facilities since EPICS had already been adopted by TPS. The Orbit Feedback System is a revitalized subsystem that now benefits from EPICS support. Additionally, the feedback computation unit has been upgraded to a Field Programmable Gate Array (FPGA), resulting in an increase in the calculating cycle from 2.5 kHz to 10 kHz. This report presents a concise overview of the integration of fast orbit feedback and the outcomes of the orbit stability enhancement following the upgrade.

Study on Beam Orbit Shift due to Synchrotron Radiation

The beam orbit stability is the crucial indicator to evaluate the performance of the synchrotron radiation source. In order to obtain higher beam quality, higher stability requirements are placed on the beam orbit. The stability can be improved through accurate measurement of beam orbit by beam position monitors (BPMs) and appropriate feedback system. However, due to radiation of the synchrotron beams on the vacuum chamber, the thermal effect of synchrotron radiation causes the thermal deformation of the vacuum chamber. The thermal deformation drives the BPM fixed on the vacuum chamber to move, which will induce error to the beam orbit. We analyze the effect of beam current on the vacuum chamber movement and the effect of vacuum chamber movement on the beam orbit. We also built an online vacuum chamber displacement measurement system on Hefei Light Source II (HLS II), which is used to validate and correct our analysis. After analysis and verification, the vacuum chamber moves with the change of current. The larger the change of current, the larger the vacuum chamber displacement. The vacuum chamber displacement has a hysteresis compared to the current change.

Global existence, blow-up and stability of standing waves for the Schrödinger-Choquard equation with harmonic potential

<abstract><p>In this article, we conduct a comprehensive investigation into the global existence, blow-up and stability of standing waves for a $ L^{2} $-critical Schrödinger-Choquard equation with harmonic potential. First, by taking advantage of the ground-state solutions and scaling techniques, we obtain some criteria for the global existence and blow-up of the solutions. Second, in terms of the refined compactness argument, scaling techniques and the variational characterization of the ground state solution to the Choquard equation with $ p_{2} = 1+\frac{2+\alpha}{N} $, we explore the limiting dynamics of blow-up solutions to the $ L^{2} $-critical Choquard equation with $ L^{2} $-subcritical perturbation, including the $ L^{2} $-mass concentration and blow-up rate. Finally, the orbital stability of standing waves is investigated in the presence of $ L^{2} $-subcritical perturbation, focusing $ L^{2} $-critical perturbation and defocusing $ L^{2} $-supercritical perturbation by using variational methods. Our results supplement the conclusions of some known works.</p></abstract>

Global stability of the interior equilibrium and the stability of Hopf bifurcating limit cycle in a model for crop pest control

<p>Mathematical modeling and analysis of a crop-pest interacting system helps us to understand the dynamical properties of the system such as stability, bifurcations and chaos. In this article, a predator-prey type mathematical model for pest control using bio-pesticides has been analysed to study the global stability property of the interior equilibrium point. Moreover, the occurrence and orbital stability of Hopf bifurcating limit cycle solutions have been studied using ref30's conditions. Analytical and numerical results show that the interior equilibrium of the pest control model is globally asymptotically stable. Also, Hopf bifurcating occurs when the bifurcation parameter crosses the critical value, and the bifurcating periodic solution is found to be stable.</p>

Existence and orbital stability results for the nonlinear Choquard equation with rotation

Existence and orbital stability results for the nonlinear Choquard equation with rotation

Орбитальная стабилизация динамически вытянутого малого космического аппарата с помощью магнитной системы ориентации

The paper proposes an algorithm for angular motion control of a dynamically elongated spacecraft. The algorithm is based on the direct Lyapunov method using matrix control coefficients. The calculated mechanical torque is implemented using a magnetic attitude control system. Control parameters are selected using Floquet theory to ensure convergence of the motion trajectory to the required one. A numerical study of controlled motion to achieve gravitational attitude equilibrium of a 3U CubeSat is carried out.

Finite element simulation of fast corrector magnets for PETRA IV

The new synchrotron light source PETRA IV at DESY will use a fast orbit feedback system with hundreds of fast corrector magnets to meet stringent orbit stability requirements. These magnets are operated at high frequencies, creating strong eddy currents that result in Joule losses and a time delay between applied voltage and aperture field. User experiments impose challenging requirements on beam operation to preserve the point of the radiation source. To meet the demanding feedback requirements, finite element simulations are needed to understand the characteristics of the corrector magnet. However, due to the small skin depths at high frequencies and the laminated structure of the yoke, these simulations need a very fine mesh and are thus very costly. Therefore, we homogenize the laminated yoke which reduces the computational effort but captures the eddy current effects accurately. The reduction of simulation times from several hours to a few minutes allows us to conduct extensive studies of the eddy current losses and the field quality of the magnets.

Design of infinite horizon LQR controller for discrete delay systems in satellite orbit control: A predictive controller and reduction method approach

In the realm of satellite orbit control, powerful controller design plays a pivotal role in minimizing fuel consumption and ensuring orbit stability. This article introduces an advanced approach to the design of a Linear Quadratic Regulator (LQR) controller with an infinite horizon, tailored for discrete delay systems. The proposed methodology integrates predictive control with a reduction method, aiming for optimality while addressing performance and system constraints. Formulating the control problem as a quadratic program, the predictive control method generates a sequence of control inputs using a reducing horizon strategy. Stability analysis, employing Lyapunov-Krasovsky functions and linear matrix inequalities, yields delay-independent conditions for exponential convergence. A numerical example showcases the controller's effectiveness in maintaining orbit and reducing fuel consumption, underlining its capacity to achieve control objectives despite uncertainties and time delays. This research contributes to robust control strategies in satellite orbit systems, enhancing control performance and operational efficiency.

ON STABILITY OF SOLITONS FOR MAXWELL–LORENTZ SYSTEM WITH SPINNING PARTICLE

Abstract. We consider stability of solitons of the Maxwell–Lorentz system with extended charged spinning particle. The solitons are solutions which correspond to a particle moving with a constant velocity v with |v| < 1 and rotating with a constant angular velocity ω, [1]–[4]. Our main results are the orbital stability of moving solitons with ω = 0 and a linear orbital stability of rotating solitons with v = 0. The Hamilton–Poisson structure of the Maxwell–Lorentz system is degenerate and admits the Casimir invariants, [1]. We construct the Lyapunov function as a linear combination of the Hamiltonian with a suitable Casimir invariant. The key point is a lower bound for this function. The proof of the bound in the case ω ≠ 0 relies on angular momentum conservation and suitable spectral arguments including the Heinz inequality and closed graph theorem

Orbital stability of the periodic peakons for the higher-order modified Camassa-Holm equation

Orbital stability of the periodic peakons for the higher-order modified Camassa-Holm equation

Optimizing Spacecraft Lifespan: Balancing Mass and Propellant Fraction

Over the decades, scholars and data scientists have extensively explored the correlation between satellite mass and its impact on satellite reliability—an essential consideration for satellite manufacturers and space agencies. Initially, a conceptual notion, a group of statisticians has now rigorously defined the reliability parameter of spacecraft across different mass categories, utilizing a survival analysis algorithm pioneered by Kaplan & Meier in 1958. J.H Saleh's analysis reveals that spacecraft in the medium-range category (with mass ranging from approximately 500-1000 kilograms) exhibits maximum reliability and a longer lifespan. This statistical model has provided a foundation for the next generation of data scientists to redefine satellite reliability models. Examining mass parameters such as spacecraft dry mass, propellant mass, and payload mass, the role of propellant mass emerges as crucial in determining spacecraft survival in various planetary orbits. Propellant facilitates trajectory raising maneuvers, course corrections, and orbital stabilization (e.g., ESA’s Cassini's final plunge due to propellant exhaustion). Therefore, integrating a larger propellant tank into a relatively small spacecraft may not extend its lifespan; in fact, it could lead to spacecraft destabilization. Maintaining an optimal propellant and spacecraft mass ratio becomes paramount for effective operations. Addressing this, an innovative mathematical and statistical model has been introduced and validated, defining a propellant mass fraction limit of 0.2 to 0.6 as optimal for longer survivability. In conclusion, the various masses of a spacecraft significantly impact its lifespan and reliability. Satellite manufacturers must carefully consider mass and mass fraction parameters during the design and validation phases to ensure the spacecraft's optimal performance before deploying it into any interplanetary orbit. This consideration remains a critical task, especially as recovering a spacecraft beyond low-earth orbit poses significant challenges

Nonlinear Rotations on a 3-Dimensional Lattice

The study of resonances of Hamiltonian systems with a divided phase space is a well-established area of research which attracted the interests of many researchers over the years. We study such resonances over a discrete space focusing on the rotational motion of some orbits in the 3-Dimensional lattice, ?3. In this study, we construct the discrete standard map from 2-Dimensional to 3-Dimensional lattices. Then, we identify and categorize any transformation that could give periodicity for the 3-Dimensional lattice on a specific map. The study aims to determine the points that give the periodicity and at the same time investigate the behavior of the points for the nonlinear stable orbits over a discrete space. For some choice of parameters ???? ?, our findings showed that the orbit of the 3-Dimensional map is periodic depending on the initial conditions. Some arbitrary initial conditions may be periodic in a 3-Dimensional lattice.Keywords: Hamiltonian systems, nonlinear rotations, space discretization, arithmetic dynamics

Update on WASP-19

Tidal interaction between a star and a close-in massive exoplanet causes the planetary orbit to shrink and eventually leads to tidal disruption. Understanding orbital decay in exoplanetary systems is crucial for advancing our knowledge of planetary formation and evolution. Moreover, it sheds light on the broader question of the long-term stability of planetary orbits and the intricate interplay of gravitational forces within stellar systems. Analyzing Transiting Exoplanet Survey Satellite (TESS) data for the ultra-short period gas giant WASP-19, we aim to measure orbital period variations and constrain the stellar tidal quality parameter. For this, we fitted the TESS observations together with two WASP-19 transits observed using the Las Cumbres Observatory Global Telescope (LCOGT) and searched for orbital decay in combination with previously published transit times. As a result, we find a deviation from the constant orbital period at the 7σ level. The orbital period changes at a rate of P˙=−3.7±0.5msyear−1, which translates into a tidal quality factor of Q★′=(7±1)×105. We additionally modeled WASP-19 b’s phase curve using the new TESS photometry and obtained updated values for the planet’s eclipse depth, dayside temperature, and geometric albedo. We estimate an eclipse depth of 520±60 ppm, which is slightly higher than previous estimates and corresponds to a dayside brightness temperature of 2400±60 K and geometric albedo of 0.20±0.04.

Axially symmetric exponential metric

We present a new family of vacuum axially symmetric static solutions to Einstein’s field equations. This solution is a geometrically modified version of the Yilmaz exponential metric (YEM) which has recently been shown to represent a traversable wormhole. This vacuum solution is a one-parameter static singular solution with its singularity located at r=0. Furthermore, it is shown that both the YEM and its geometrically modified version, introduced in this work i.e., the Axially Symmetric Exponential metric (ASEM) belong to a general 2-parameter class of solutions supported by an anisotropic fluid. Depending on the parameters the generic energy–momentum tensor represents either an exotic or a normal fluid. Concerning the ASEM, the circular stable orbit does not exist for a null particle, however, for a massive particle such orbit exists provided its radius is larger than a minimum radius. This is in analogy with the Schwarzschild black hole as well as the YEM.

Statistical mechanical characterization of billiard systems

Area-preserving maps play an important role in diverse fields as they are widely used for modeling complex systems. In addition, these maps provide rich observations by presenting stable orbits and chaotic behavior separately or together in the phase space depending on the control parameter. In recent years, several studies on these maps, drawing inspiration from the phase space dynamics, have shown that nonextensive statistical mechanics provides appropriate instruments to characterize these systems. In this study, we perform a rigorous numerical analysis to delve into the statistical mechanical properties of a billiard system. Our primary goal is to confirm the presence of a q-Gaussian distribution, with an estimated q value of approximately 1.935. We accomplish this by examining the probability distribution of the cumulative sum of system iterates, focusing specifically on initial conditions within the stability islands. Our findings align seamlessly with the latest research in this field. Furthermore, we show that a multi-component probability distribution containing both Gaussian and q-Gaussians describes the entire system for some parameter regions where the phase space consists of stability islands together with the chaotic sea.

Theoretical analysis of co-existing periodic orbits in sparse binary neural networks

A sparse binary neural network is a discrete-time recurrent neural network characterized by local binary connections and signum-type neuron models. The dynamics is described by an autonomous difference equation of binary state variables. Depending on the parameters, the network generates various periodic orbits of binary vectors. Multiple periodic orbits can co-exist and the network exhibits one of them depending on initial condition. Real/potential applications of the periodic orbits include control signals of switching circuits and basic signals for time-series approximation. The network is well suited for theoretical analysis and simple hardware implementation. This paper considers shift-type periodic orbits in the networks. As the main theoretical results, we clarify the number, period, and stability of the periodic orbits for key parameters. As a first step to the applications in the future, we present an FPGA-based hardware prototype and confirm typical periodic orbits experimentally.

Fractal Architecture of the Universe Based on Primary-Centric World-View - A Post Copernican Conjecture

This paper investigates the fractal architecture of our Universe based on Primary-Centric Theoretical Formulation. Through theoretical analysis of Earth-Moon System, I arrived at the planetary satellite dynamics which was found to apply equally well to Solar and Exo-solar systems. This gave the theoretical foundation of the New Perspective of the birth and evolution of Exo-solar Systems. This was further extended to the theoretical analysis of star pairs and Neutron-Star pairs. This laid down the Primarycentric World View which I postulate as the physical process which has been shaping the evolution of the Universe and the hot-spots of the Cosmic Microwave Background Radiation right from 380,000 yrs after the Big Bang to date in top-down model resulting into Super-clusters, Clusters, Galaxies and Solar Systems. Primary-centric analysis corresponds to keplerian Analysis for negligibly small mass ratio less than 0.001. In the Copernican Framework, Kepler’s Third Law places no restriction on the orbit of the secondary component in a celestial pair. In Primary Centric Framework there is a very definite constraint on the permitted stable orbit, introduced due to periodic tidal deformations . There are two Clarke’s Orbits which are fully circularized and synchronized and hence nondissipative and equilibrium orbits called inner and outer Clarke's orbits equivalent to two geosynchronous orbits in Earth-Moon scenario. Outer Clarke’s Orbit is permissible as a stable orbit if the mass ratio of secondary to primary is greater than 0.2, Inner Clarke’s Orbit is permissible if mass ratio is less than 10-4 . If the mass ratio is between 10-4 to 0.2 then secondary spirals-out from inner Clarke’s Orbit to outer Clarke’s Orbit if it tumbles into super-synchronous orbit and spirals-in if it tumbles into sub-synchronous orbit destined to be destroyed by the primary. My conjecture states that every cosmological sub-system has a Monarch (or dominant) Primary (M_primary) Component anchoring the given sub-system and this Primary decides the stable equilibrium orbits of the secondary/secondaries. Planet-Satellite has a Planet as the M_primary, Solar System and exo-Solar Systems have a planet hosting star (PHS) as the M_primary, Galaxy has a Super-Massive Black Hole(SMBH) as the M_primary, Cluster has a cD galaxy (central dominant Galaxy) which is also known as Brightest Cluster Galaxy(BCG) as the M_primary, Super-Cluster has a massive Cluster hosting a QUASER/Blazer as the M_primary. This goes adinfinitum until a Cosmic Web is woven with Cosmic filaments. This conjecture gains a definite credence after the recent discoveries of the over-massive Black Holes in M_Galaxies namely Messier 87 in Virgo Cluster, NGC 3842 in Leo Cluster, NGC 4889 in Coma Cluster[68] and NGC 1277 in Perseus Cluster[66] which had been proposed as M_Galaxies on general considerations even before the confirmation of over-massive black holes. In 2011, a group of floating planets have been discovered. This is a transitory event and is an exception to this conjecture.

Isotopic trichotomy of main belt asteroids from implantation of outer solar system planetesimals

Recent analyses of samples from asteroid (162173) Ryugu returned by JAXA's Hayabusa2 mission suggest that Ryugu and CI chondrites formed in the same region of the protoplanetary disk, in a reservoir that was isolated from the source regions of other carbonaceous (C-type) asteroids. Here we conduct N-body simulations in which CI planetesimals are assumed to have formed in the Uranus/Neptune zone at ∼15–25 au from the Sun. We show that CI planetesimals are scattered by giant planets toward the asteroid belt where their orbits can be circularized by aerodynamic gas drag. We find that the dynamical implantation of CI asteroids from ∼15–25 au is very efficient with ∼5% of ∼100-km planetesimals reaching stable orbits in the asteroid belt by the end of the protoplanetary gas disk lifetime. The efficiency is reduced when planetesimal ablation is accounted for. The implanted population subsequently evolved by collisions and was depleted by dynamical instabilities. The model can explain why CIs are isotopically distinct from other C-type asteroids which presumably formed at ∼5–10 au.

Radiation properties of the accretion disk around a black hole in Einstein-Maxwell-scalar theory* *Supported by the National Natural Science Foundation of China (11675143, 11975203) and the National Key Research and Development Program of China (2020YFC2201503)

In this study, we explore the properties of a non-rotating black hole in the Einstein-Maxwell-scalar (EMS) theory and investigate the luminosity of the accretion disk surrounding it. We determine all the orbital parameters of particles in the accretion disk, including the radius of the innermost stable circular orbit (ISCO) with angular velocity, angular momentum, and energy. Further, we study the radiative efficiency for different values of black hole parameters. Finally, we analyze the flux, differential luminosity, and temperature of the accretion disk.

3:1/3:2 Resonant orbits touring L3–L5 in cislunar space

The aim of this study is to explore the space environment near the Lagrange points (L3–L5) in cislunar space using 3:1/3:2 resonant orbital families that can travel in the vicinity of L3–L5. First, the planar and spatial 3:1/3:2 resonant orbital families symmetrical about the x-axis are computed using the continuation method in the circular restricted Earth-Moon three-body problem. Then, the characteristics of the two resonant orbital families are analyzed, including the variation in Kepler orbital elements, apogee direction, Jacobian constant, and distances from apogees to L3–L5 as well as the orbital stability analyzed by the dynamic theory. Furthermore, the correlation between shadow duration and orbit inclination including the strategy for shadow avoidance are proposed based on the Sun-Earth-Moon bicircular restricted four-body problem. The advantages of 3:1/3:2 resonant orbits used in this study are stability, shadow avoidance and L3–L5 tour capability, and potential applications in the cislunar space.