Search Results (125)

Continuous low thrust is widely used in orbit transfer maneuvers. If the unknown maneuvers are not correctly compensated, the orbiting accuracy will be seriously affected. We propose a rapid method for pre-identifying thrust acceleration based on single-arc orbit determination in order to determine the orbit of non-cooperative continuous low-thrust maneuvering spacecraft. The single-arc orbit determination results of two ground-based radar observations with a certain time interval are used to inversely determine the direction and magnitude of acceleration of the spacecraft under continuous thrust based on their relationship with satellite orbit parameters. The solution error is relatively small when using this method, even over a short period of time when data are sparse. The results can then be applied to the orbital adjustment of a satellite. The results show that when the satellite climbs with maximum tangential acceleration, the interval between the two radar observations is greater than 7 h, and the proposed method can rapidly pre-identify tangential thrust acceleration with a solution error of less than 5%. When the satellite adjusts the orbital plane with the maximum normal acceleration, the average relative measurement error of the normal acceleration is about 20% when the time interval between two observations is 24 h. The longer the observation interval and the greater the thrust acceleration, the smaller the relative error. The calculation results can be used as the initial value for precision orbit determination of continuous low-thrust maneuvering spacecraft. Full article

The three-tiered microbial food chain without maintenance under leachate recirculation is the subject of a mathematical seven-dimensional dynamical system that is proposed in this work. This model captures the complex interactions between chlorophenol degraders, phenol degraders, and methanogens in the presence of hydrogen inhibition. The implementation allows for investigation of how hydrogen levels affect the overall system dynamics and phenol production. There is a thorough qualitative analysis provided. A stability analysis of equilibrium points is performed. It is demonstrated that the persistence of the three bacteria is correlated with the existence of the positive equilibrium point, assuming some monotonicity properties on the growth rates. Asymptotic coexistence is satisfied, although periodic orbit possibilities are not ruled out. In order to decrease the amount of organic materials within the reactor, we suggest an optimal strategy on the rate of leachate recirculation in the second stage. Lastly, we offer a few numerical investigations that support and strengthen the theoretical conclusions. Full article

To study the orbits of satellites, a galaxy can be modeled either by means of a static gravitational potential or by live N-body particles. Analytic potentials allow for fast calculations but are idealized and non-responsive. On the other hand, N-body simulations are more realistic but demand higher computational cost. Our goal is to characterize the regimes in which analytic potentials provide a sufficient approximation and those where N-bodies are necessary. We perform two sets of simulations, using both Gala and Gadget, in order to closely compare the orbital evolution of satellites around a Milky Way-like galaxy. Focusing on the periods when the satellite has not yet been severely disrupted by tidal forces, we find that the orbits of satellites up to ${10}^8{\mathrm{M}}_{\odot }$ can be reliably computed with analytic potentials to within 5% error if they are circular or moderately eccentric. If the satellite is as massive as ${10}^9{\mathrm{M}}_{\odot }$ then errors of 9% are to be expected. However, if the orbital radius is smaller than 30 kpc then the results may not be relied upon with the same accuracy beyond 1–2 Gyr. Full article

Objectives: Although considered a safe procedure, functional endoscopic sinus surgery (FESS) can cause various significant ophthalmic complications, i.e., serious extraocular muscle (EOM) damage. The aim of this study is to review the surgical management outcomes of patients with mechanical strabismus and diplopia as a complication of FESS, who referred to ophthalmological department in Norbert Barlicki University Teaching Hospital No. 1 over the 5-year period from 2018 to 2023. Methods: The records of seven consecutive patients with diplopia following endoscopic sinus surgery were retrospectively reviewed. Demographics, ophthalmological and orthoptic examination, the results of orbital imaging, type of FESS, type of strabismic surgery, and the timing of the first intervention were analysed. Results: The time from FESS to referral for strabismic intervention varied from one day to two months. Two patients, who were operated upon immediately after the FESS procedure, underwent direct reunion of the proximal and distal parts of the ruptured medial rectus muscle. One patient required maxillofacial intervention in order to improve prominent enophthalmos. The remaining five demonstrated severe adhesion formation around at least one of the EOMs and orbital walls. Only patients who were operated upon within a short period after complicated FESS achieved orthotropia and lack of diplopia in the primary position with a single surgery. Conclusions: Early recognition of the orbital complications subsequent to FESS and prompt referral are essential for achieving a satisfactory surgical result. Appropriate treatment should be based on the mechanism, location, type, and severity of muscle damage. Full article

In the Moon–Earth elliptic restricted three-body problem, near-polar and near-circular lunar-type periodic orbits are numerically continued from Keplerian circular orbits using Broyden’s method with line search. The Hamiltonian system, expressed in Cartesian coordinates, is treated via the symplectic scaling method. The radii of the initial Keplerian circular orbits are then scaled and normalized. For cases in which the integer ratios $\{j/k\}$ of the mean motions between the inner and outer orbits are within the range $[9,150]$, some periodic orbits of the elliptic restricted three-body problem are investigated. For the middle-altitude cases with $j/k\in [38,70]$, the perturbations due to $J_2$ and $C_{22}$ are incorporated, and some new near-polar periodic orbits are computed. The orbital dynamics of these near-polar, near-circular periodic orbits are well characterized by the first-order double-averaged system in the Poincaré–Delaunay elements. Linear stability is assessed through characteristic multipliers derived from the fundamental solution matrix of the linear varational system. Stability indices are computed for both the near-polar and planar near-circular periodic orbits across the range $j/k\in [9,50]$. Full article

This paper investigates the fly-around formation between the servicer spacecraft and the target spacecraft. Inspired by the spacecraft orbital motion under the Earth’s gravity, an intuitive, analytical guidance law for spatial fly-around formation design with the low-thrust maneuver is proposed. Beginning with the relative translational dynamics based on relative position and velocity, the control input of the guidance law is designed to contain two parts. The first part is the feed-forward term, which makes the relative dynamics a second-order integration model. The second part is the artificial gravity term, which has similar expressions to the Earth’s gravity, and includes the artificial gravitational coefficient and the vector of the artificial gravity center. The above two parameters can be designed to determine the size, shape, and period of the fly-around trajectory. Specifically, three kinds of fly-around trajectories are discussed in detail. The first two are the spatial ellipses with the target spacecraft locating at the focus and the center of the ellipses, respectively. The third is the spatial circle. The proposed method can be easily extended to the design of planar fly-around formation, which is very systematic and comprehensive, and the fuel consumption of the control input is specifically discussed. Numerical simulations are conducted to demonstrate the efficiency of the proposed method. Full article

Super-Earth b and sub-Neptunes c and d are orbiting about the M3.0V dwarf TOI-270 in that order from the star. Their global resonant chain (3:5, 1:1, 2:1) is extremely surprising because planet d appears to be the only known planet occupying the 2:1 resonant orbit without participating in a Laplace resonance (LR) or another planet intervening between the 1:1 and 2:1 orbits as in HD 110067. We do not believe that TOI-270 d is an exception to the empirical rule calling for 2:1 vacancy except in 1:2:4 LRs and Laplace-like 2:3:4 chains. Instead, a LR might exist in this system, and we searched (to no avail) the TESS light curves of TOI-270 for hints of an outer planet that would complete the LR chain. Alternative explanations would be an unknown planet more massive than planet c ($M_{\mathrm{c}}=6.20M_{\oplus }$) establishing the actual 1:1 orbit, or planet b residing in the 1:2 Laplace orbit with a period shorter by 0.53 days. However, these possibilities are ruled out by current data. This leaves only one other option to explore: the observed orbits could be in a stable ${\displaystyle \frac{3}{5}}$:1:2 resonant chain. Preliminary calculations do not preclude this possibility that should be investigated further by numerical orbit integrations. To this end, we determine two potentially resonant angles, $\phi$ and $\widehat{\phi }$, related via the Laplace phase ${\phi }_{\mathrm{L}}$ by $\widehat{\phi }={\phi }_{\mathrm{L}}+2\phi$. In contrast, HD 110067 is shown to have planets d-e-f in a Laplace-like 1:${\displaystyle \frac{3}{2}}$:2 resonance with phase $\phi =2{\phi }_{\mathrm{L}}$ precisely. Full article

The Melnikov method is applied to a class of generalized Ziegler pendulums. We find an analytical form for the separatrix of the system in terms of Jacobian elliptic integrals, holding for a large class of initial conditions and parameters. By working in Duffing approximation, we apply the Melnikov method to the original Ziegler system, showing that the first non-vanishing Melnikov integral appears in the second order. An explicit expression for the Melnikov integral is derived in the presence of a time-periodic external force and for a suitable choice of the parameters, as well as in the presence of a dissipative term acting on the lower rod of the pendulum. These results allow us to define fundamental relationships between the Melnikov integral and a proper control parameter that distinguishes between regular and chaotic orbits for the original dynamical system. Finally, in the appendix, we present proof of a conjecture concerning the non-validity of Devaney’s chaoticity definition for a discrete map associated with the system. Full article

The present paper focuses on some classes of dynamical systems involving Hamilton–Poisson structures, while neglecting their chaotic behaviors. Based on this, the closed-form solutions are obtained. These solutions are derived using the Optimal Auxiliary Functions Method (OAFM). The impact of the physical parameters of the system is also investigated. Periodic orbits around the equilibrium points are performed. There are homoclinic or heteroclinic orbits and they are obtained in exact form. The dynamical system is reduced to a second-order nonlinear differential equation, which is analytically solved through the OAFM procedure. The influence of initial conditions on the system is explored, specifically regarding the presence of symmetries. A good agreement between the analytical and corresponding numerical results is demonstrated, reflecting the accuracy of the proposed method. A comparative analysis underlines the advantages of the OAFM compared with the iterative method. The results of this work encourage the study of dynamical systems with bi-Hamiltonian structure and similar properties as physical and biological problems. Full article

The lunar south pole has gained significant attention due to its unique scientific value and potential for supporting future human exploration. Its potential water ice reservoirs and favourable conditions for long-term habitation make it a strategic target for upcoming space missions. This has led to a continuous increase in missions towards the Moon thanks mainly to the boost provided by NASA’s Artemis programme. This study focuses on designing a satellite constellation to provide communication coverage for the lunar south pole. Among the various cislunar orbits analysed, the halo orbit families near Earth–Moon Lagrangian points L1 and L2 emerged as the most suitable ones for ensuring continuous communication while minimising the number of satellites required. These orbits, first described by Farquhar in 1966, allow spacecraft to maintain constant communication with Earth due to their unique geometric properties. The candidate orbits were initially implemented in MATLAB using the Circular Restricted Three-Body Problem (CR3BP) to analyse their main features such as stability, periodicity, and coverage time percentage. In order to develop a more detailed and realistic scenario, the obtained initial conditions were refined using a full ephemeris model, incorporating a ground station located near the Connecting Ridge Extension to evaluate communication performance depending on the minimum elevation angle of the antenna. Different multi-body constellations were propagated; however, the constellation consisting of three satellites around L2 and a single satellite around L1 turned out to be the one that best matches the coverage requirements. Full article

We prove a conjecture on the second minimal odd periodic orbits with respect to Sharkovski ordering for the continuous endomorphisms on the real line. A $(2k+1)$-periodic orbit $\{{\beta }_1<{\beta }_2<\cdots <{\beta }_{2k+1}\}$, ($k\ge 3$) is called second minimal for the map f, if $2k-1$ is a minimal period of ${f|}_{[{\beta }_1,{\beta }_{2k+1}]}$ in the Sharkovski ordering. Full classification of second minimal orbits is presented in terms of cyclic permutations and directed graphs of transitions. It is proved that second minimal odd orbits either have a Stefan-type structure like minimal odd orbits or one of the $4k-3$ types, each characterized with unique cyclic permutations and directed graphs of transitions with an accuracy up to the inverses. The new concept of second minimal orbits and its classification have an important application towards an understanding of the universal structure of the distribution of the periodic windows in the bifurcation diagram generated by the chaotic dynamics of nonlinear maps on the interval. Full article

It is well known that mean elements obtained by canonical perturbation theory only agree partially with the average dynamics of the osculating orbit. While this fact does not necessarily compromise the accuracy of corresponding perturbation solutions, the loose use of the terminology “mean elements” in artificial satellite theory may obscure the understanding of the variety of available solutions in the literature, and thus make the implementation of additional patches to increase their performance ambiguous. We resort to noncanonical perturbation methods, and, for the main problem of artificial satellite theory (the $J_2$-problem), compute the purely periodic, noncanonical, mean-to-osculating transformation that yields the exact separation between short- and long-period variations up to the second order of the zonal harmonic of the second degree. To our knowledge this transformation is new and was long-awaited by software developers in order to improve operational orbit propagation tools based on semianalytical integration. It is also shown that this kind of noncanonical solution confines the long-period oscillations of the semimajor axis in the mean variation equations. Full article

Fullerenes are a class of highly symmetric spherical carbon materials that have attracted significant attention in optoelectronic applications due to their excellent electron transport properties. However, the isotropy of their spherical structure often leads to disordered inter-sphere stacking in practical applications, limiting in-depth studies of their electron transport behavior. The successful fabrication of long-range ordered two-dimensional fullerene arrays has opened up new opportunities for exploring the structure–activity relationship in spatial charge transport. In this study, theoretical calculations were performed to analyze the effects of different periodic arrangements in two-dimensional fullerene arrays on electronic excitation and optical behavior. The results show that HLOPC₆₀ exhibits a strong absorption peak at 1050 nm, while TLOPC₆₀ displays prominent absorption features at 700 nm and 1300 nm, indicating that their electronic excitation characteristics are significantly influenced by the periodic structure. Additionally, analyses of orbital distribution and the spatial electron density reveal a close relationship between carrier transport and the structural topology. Quantitative studies further indicate that the interlayer interaction energies of the HLOPC₆₀ and TLOPC₆₀ arrangements are −105.65 kJ/mol and −135.25 kJ/mol, respectively. TLOPC₆₀ also exhibits stronger dispersion interactions, leading to enhanced interlayer binding. These findings provide new insights into the structural regulation of fullerene materials and offer theoretical guidance for the design and synthesis of novel organic optoelectronic materials. Full article

System stability control in resource allocation is a critical issue in group robot systems. Against this backdrop, this study investigates the nonlinear dynamics and chaotic phenomena that arise during pricing games among finitely rational group robots and proposes control strategies to mitigate chaotic behaviors. A system model and a business model for group robots are developed based on market mechanism mapping, and the dynamics of resource allocation are formulated as a second-order discrete nonlinear system using game theory. Numerical simulations reveal that small perturbations in system parameters, such as pricing adjustment speed, product demand coefficients, and resource substitution coefficients, can induce chaotic behaviors. To address these chaotic phenomena, a control method combining state feedback and parameter adjustment is proposed. This approach dynamically tunes the state feedback intensity of the system via a control parameter M, thereby delaying bifurcations and suppressing chaotic behaviors. It ensures that the distribution of system eigenvalues satisfies stability conditions, allowing control over unstable periodic orbits and period-doubling bifurcations. Simulation results demonstrate that the proposed control method effectively delays period-doubling bifurcations and stabilizes unstable periodic orbits in chaotic attractors. The stability of the system’s Nash equilibrium is significantly improved, and the parameter range for equilibrium pricing is expanded. These findings provide essential theoretical foundations and practical guidance for the design and application of group robot systems. Full article

In order to improve the current standard of analysis-ready Synthetic Aperture Radar (SAR) backscatter data, we introduce a machine learning-based approach to estimate the slope of the backscatter–incidence angle relationship from several backscatter statistics. The method requires information from radiometric terrain-corrected gamma nought time series and overcomes the constraints of a limited orbital coverage, as exemplified with the Sentinel-1 constellation. The derived slope estimates contain valuable information on scattering characteristics of different land cover types, allowing for the correction of strong forward-scattering effects over water bodies and wetlands, as well as moderate surface scattering effects over bare soil and sparsely vegetated areas. Comparison of the estimated and computed slope values in areas with adequate orbital coverage shows good overall agreement, with an average RMSE value of 0.1 dB/° and an MAE of 0.05 dB/°. The discrepancy between RMSE and MAE indicates the presence of outliers in the computed slope, which are attributed to speckle and backscatter fluctuations over time. In contrast, the estimated slope excels with a smooth spatial appearance. After correcting backscatter values by normalising them to a certain reference incidence angle, orbital artefacts are significantly reduced. This becomes evident with differences up to 5 dB when aggregating the normalised backscatter measurements over certain time periods to create spatially seamless radar backscatter composites. Without being impacted by systematic differences in the illumination and physical properties of the terrain, these composites constitute a valuable foundation for land cover and land use mapping, as well as bio-geophysical parameter retrieval. Full article