Orbital Resonance Research Articles

Stream Fanning and Bifurcations: Observable Signatures of Resonances in Stellar Stream Morphology

Recent observations have revealed a trove of unexpected morphological features in many of the Milky Way’s stellar streams. Explanations for such features include time-dependent deformations of the Galactic gravitational potential, local disruptions induced by dark matter substructure, and special configurations of the streams’ progenitors. In this paper, we study how these morphologies can also arise in certain static, nonspherical gravitational potentials that host a subset of resonantly trapped orbit families. The transitions, or separatrices, between these orbit families mark abrupt discontinuities in the orbital structure of the potential. We develop a novel numerical approach for measuring the libration frequencies of resonant and near-resonant orbits and apply it to study the evolution of stellar streams on these orbits. We reveal two distinct morphological features that arise in streams on near-resonant orbits: fans, which come about due to a large spread in the libration frequencies near a separatrix, and bifurcations, which arise when a separatrix splits the orbital distribution of the stellar stream between two (or more) distinct orbit families. We demonstrate that these effects can arise in some Milky Way streams for certain choices of the dark matter halo potential and discuss how this might be used to probe and constrain the global shape of the Milky Way’s gravitational potential.

Maps of Solar Wind Plasma Precipitation onto Mercury’s Surface: A Geographical Perspective

Mercury is the closest planet to the Sun, possesses a weak intrinsic magnetic field, and has only a very tenuous atmosphere (exosphere). These three conditions result in a direct coupling between the plasma emitted from the Sun (namely, the solar wind) and Mercury’s surface. The planet’s magnetic field leads to a nontrivial pattern of plasma precipitation onto the surface that is expected to contribute to the alteration of the regolith over geological timescales. The goal of this work is to study the solar wind plasma precipitation onto the surface of Mercury from a geographical perspective, as opposed to the local time-of-day approach of previous precipitation modeling studies. We employ solar wind precipitation maps for protons and electrons from two fully kinetic numerical simulations of Mercury’s plasma environment. These maps are then integrated over two full Mercury orbits (176 Earth days). We found that the plasma precipitation pattern at the surface is most strongly affected by the upstream solar wind conditions, particularly the interplanetary magnetic field direction, and less by Mercury’s 3:2 spin–orbit resonance. We also found that Mercury’s magnetic field is able to shield the surface from roughly 90% of the incoming solar wind flux. At the surface, protons have a broad energy distribution from below 500 eV to more than 1.5 keV, while electrons are mostly found in the range 0.1–10 keV. These results will help to better constrain space weathering and exosphere source processes at Mercury, as well as interpret observations by the ongoing ESA/JAXA BepiColombo mission.

Supraequatorial displacement with lateral rectus myopexy for treatment of myopic sagging/heavy eye

PurposeTo describe the outcome of the patients diagnosed of sagging/heavy eye associated to myopia, that were operated on with the supra-equatorial displacement with LR myopexy. MethodsA retrospective study of 9 cases between 2017−2023. The following data were analyzed: horizontal and vertical deviation, diplopia, amblyopia, ductions, ocular torsion, sensorial test, macular pathology, and the orbital magnetic resonance. Treatment was considered Successful if the diplopia was improved or eliminated and a final vertical deviation (VD) ≤5 prism diopters (PD). ResultsThe mean age (SD) was: 62.11 (4.6) years (100% women). A total of 88.88% presented diplopia. The mean preoperative hypotropia was: 11.33 PD (SD 3.16), and the mean final VD 3.44 PD (SD 3.05). After surgery, the hypotropia was overcorrected in one case, under corrected in 5, and orthophoria was achieved in another three. The technique was associated with surgery of another rectus muscle in 4 subjects. The mean follow-up time after surgery was 34 months (SD 34.62). Six of the 9 patients improved with a vertical deviation ≤5 PD. In 3 patients, the diplopia was eliminated, while in 5 it remained intermittent (three with macular pathology). ConclusionSupra-equatorial displacement with LR myopexy for treatment of myopic sagging/heavy eye, is a therapeutic option if hypotropia is less than 12 PD or the Yokoyama technique is not indicated. A good result was obtained in most cases, although diplopia could only be totally suppressed in three, and another five remained intermittent.

Is There an Earth-like Planet in the Distant Kuiper Belt?

The orbits of trans-Neptunian objects (TNOs) can indicate the existence of an undiscovered planet in the outer solar system. Here we used N-body computer simulations to investigate the effects of a hypothetical Kuiper Belt planet (KBP) on the orbital structure of TNOs in the distant Kuiper Belt beyond ∼50 au. We used observations to constrain model results, including the well-characterized Outer Solar System Origins Survey (OSSOS). We determined that an Earth-like planet (m ∼ 1.5–3 M ⊕) located on a distant (semimajor axis a ∼ 250–500 au, perihelion q ∼ 200 au) and inclined (i ∼ 30°) orbit can explain three fundamental properties of the distant Kuiper Belt: a prominent population of TNOs with orbits beyond Neptune’s gravitational influence (i.e., detached objects with q > 40 au), a significant population of high-i objects (i > 45°), and the existence of some extreme objects with peculiar orbits (e.g., Sedna). Furthermore, the proposed KBP is compatible with the existence of identified gigayear-stable TNOs in the 2:1, 5:2, 3:1, 4:1, 5:1, and 6:1 Neptunian mean motion resonances. These stable populations are often neglected in other studies. We predict the existence of an Earth-like planet and several TNOs on peculiar orbits in the outer solar system, which can serve as observationally testable signatures of the putative planet’s perturbations.

A Six-planet Resonance Chain in K2-138?

The K2-138 system hosts six planets and presents an interesting case study due to its distinctive dynamical structure. Its five inner planets are near a chain of 3/2 two-body mean-motion resonances, while the outermost body (planet g) is significantly detached, having a mean-motion ratio of n f/n g ∼ 3.3 with its closest neighbor. We show that the orbit of m g is actually consistent with the first-order three-planet resonance (3P-MMR) characterized by the relation 2n e − 4n f + 3n g = 0 and is the first time a pure first-order 3P-MMR has been found in a multiplanet system and tied to its current dynamical structure. Adequate values for the masses allow one to trace the dynamical history of the system from an initial capture in a six-planet chain (with n f/n g in a 3/1 resonance) up to its current configuration due to tidal interactions over the age of the star. The increase in resonance offset with semimajor axis, as well as its large value for n f/n g, can be explained by the slopes of the pure three-planet resonances in the mean-motion ratio plane. The triplets slide outward over these curves when the innermost pair is pulled apart by tidal effects, in a pantograph-like manner. The capture into the 3P-MMR is found to be surprisingly robust given similar masses for m g and m f, and it is possible that the same effect may also be found in other compact planetary systems.

Dynamical characterization of the 6/1 mean motion resonance between Quaoar’s ring and Weywot

ABSTRACT Recently, it has been reported the discovery of a dense ring around the trans-Neptunian object 50000 Quaoar. The ring particles seem to be very close to the 6/1 mean motion resonance with Weywot, the only known satellite in the system. In this work, we investigate the dynamical environment in the close vicinity of the 6/1 orbital resonance in the context of the restricted three-body problem. We aim to analyse whether, in view of observational constraints, the ring could be effectively evolving in resonant motion with the satellite. Through the technique of dynamical maps we identify and characterize the 6/1 mean motion resonance, finding that the main location of the resonance deviates by only 29 km from the central part of the ring. This difference lies within the 3σ confidence level, considering the uncertainties in the observational parameters. We also show that the Weywot’s eccentricity plays a significant role in the dynamical structure of the 6/1 resonance. The results show that the resonance width is smaller than the estimated ring’s width. Under assumption of a ring with eccentricity smaller than 0.05, clumping of test particles appears at the position of the different resonant multiplets, considering the nominal value of Weywot’s eccentricity. This is in agreement with observations, which indicate that the estimated resonance width (≤10 km) is comparable with the narrow and dense arc of material within Quaoar’s ring. Our results may be an indicative that the 6/1 resonance plays a key role in confining the arc ring.

Galactic Bar Resonances with Diffusion: An Analytic Model with Implications for Bar–Dark Matter Halo Dynamical Friction

The secular evolution of disk galaxies is largely driven by resonances between the orbits of “particles” (stars or dark matter) and the rotation of non-axisymmetric features (spiral arms or a bar). Such resonances may also explain kinematic and photometric features observed in the Milky Way and external galaxies. In simplified cases, these resonant interactions are well understood: for instance, the dynamics of a test particle trapped near a resonance of a steadily rotating bar is easily analyzed using the angle-action tools pioneered by Binney, Monari, and others. However, such treatments do not address the stochasticity and messiness inherent to real galaxies—effects that have, with few exceptions, been previously explored only with complex N-body simulations. In this paper, we propose a simple kinetic equation describing the distribution function of particles near an orbital resonance with a rigidly rotating bar, allowing for diffusion of the particles’ slow actions. We solve this equation for various values of the dimensionless diffusion strength Δ, and then apply our theory to the calculation of bar–halo dynamical friction. For Δ = 0, we recover the classic result of Tremaine and Weinberg that friction ultimately vanishes, owing to the phase mixing of resonant orbits. However, for Δ > 0, we find that diffusion suppresses phase mixing, leading to a finite torque. Our results suggest that stochasticity—be it physical or numerical—tends to increase bar–halo friction, and that bars in cosmological simulations might experience significant artificial slowdown, even if the numerical two-body relaxation time is much longer than a Hubble time.

ExoMMR: A New Python Package to Confirm and Characterize Mean Motion Resonances

The study of orbital resonances allows for the constraint of planetary properties of compact systems. We can predict a system’s resonances by observing the orbital periods of the planets, as planets in or near mean motion resonance (MMR) have period ratios that reduce to a ratio of small numbers. However, a period ratio near commensurability does not guarantee a resonance; we must study the system’s dynamics and resonant angles to confirm resonance. Because resonances require in-depth study to confirm, and because two-body resonances require a measurement of the eccentricity vector which is quite challenging, very few resonant pairs or chains have been confirmed. We thus remain in the era of small-number statistics, not yet able to perform large population synthesis or informatics studies. To address this problem, we build a python package to find, confirm, and analyze MMRs, primarily through N-body simulations. We then analyze all near-resonant planets in the Kepler/K2 and TESS catalogs, confirming over 60 new resonant pairs and various new resonant chains. We additionally demonstrate the package’s functionality and potential by characterizing the mass–eccentricity degeneracy of Kepler-80g, exploring the likelihood of an exterior giant planet in Kepler-80, and constraining the masses of planets in Kepler-305. We find that our methods overestimate the libration amplitudes of the resonant angles and struggle to confirm resonances in systems with more than three planets. We identify various systems that are likely resonant chains but that we are unable to confirm, and highlight next steps for exoplanetary resonances.

Cat-scratch disease manifesting as uveitis and binocular fundus nodular lesions: a case report

BackgroundCat-scratch disease typically presents with various ocular manifestations such as uveitis, vitritis, retinitis, retinochoroiditis, and optic neuritis. However, fundus nodular lesions was rarely reported. In our study, we reported a case of Cat-Scratch disease with binocular fundus nodular lesions.Case presentationAn 11-year old male presented with uveitis in the right eye and bilateral fundus nodular lesions after indirect contact with unvaccinated cats. Comprehensive ancillary examinations including wide-angle fundus photography, ultrasonography, fluorescein fundus angiography, optical coherence tomography, and orbital magnetic resonance imaging were performed to elucidate the multidimensional features of the binocular lesions. Metagenomics next-generation sequencing was utilized to confirm the diagnosis of Cat-scratch disease. The patient’s condition showed improvement after a 6-month combination treatment regimen involving systemic administration of doxycycline hyclate and methylprednisolone tablets, as well as local application of mydriatic and corticosteroid eye drops.ConclusionsWe firstly reported a case of Cat-scratch disease presenting simultaneously with uveitis and fundus nodular lesions caused by Bartonella henselae infection in a child. Timely diagnosis and treatment with antibiotics and corticosteroids showed promising outcomes for the prognosis of these ocular disorders.

Dynamics around non-spherical symmetric bodies: II. The case of a prolate body

ABSTRACT Dynamic exploration around non-spherical bodies has increased in recent decades due to the interest in studying the motion of spacecraft orbits, moons, and particle ring around these bodies. The dynamic structure around these objects is defined by regular and chaotic regions. The Poincaré surface of section technique allows mapping these regions, identifying the location of resonances, and the size of regular and chaotic zones, thus helping us to understand the dynamics around these bodies. Using this technique, we map in the a–e space the stable and unstable regions around ellipsoidal bodies, such as the dwarf planet Haumea, the centaur Chariklo, and other five hypothetical bodies, in which we keep part of the physical parameters of Haumea but we varied its period of rotation and ellipticity, to analyse the impact of these alterations in the extensions of the stable and unstable regions due to first kind orbits and spin-orbit type resonances. We identified a large region of stability, in semimajor axis and eccentricity, due to the first kind orbits. Periodic orbits of the first kind are present in a large semimajor axis interval for all considered systems and have almost zero eccentricity, while resonant and quasi-periodic orbits have high eccentricities. Furthermore, we identified the bifurcation of the 2:6 resonance when there is a spin reduction of a body with the same physical parameters as Haumea. This bifurcation generates a chaotic region, reducing the extension of the stability zone.

MRI features for prediction of the intravenous chemotherapy effect in patients with retinoblastoma

To investigate the value of orbital magnetic resonance imaging (MRI) features in predicting the efficacy of intravenous chemotherapy (IVC) for patients with retinoblastoma (RB). The pretreatment clinical and MRI data of 100 eyes from 80 RB patients who underwent IVC were collected retrospectively. There were 59 eyes in the effective group and 41 eyes in the ineffective group, and the baseline data of the two groups were compared statistically. Three radiologists reviewed and evaluated each lesion independently based on 25 MRI features. The predictive values of the MRI features for IVC efficacy were assessed by multi-factor logistic regression analysis, and their odds ratios (ORs) and 95% confidence intervals (95% CIs) were calculated. Receiver operating characteristic curves (ROCs) with the area under the curve (AUC) were used to determine the predictive abilities. A predictive model was constructed by integrating all independent predictors visualised by the nomogram. There were no statistically significant differences in sex or age between the effective and ineffective groups. The results of multivariate regression analysis showed that laterality, margin, and anterior eye segment enhancement were identified as independent factors that could predict IVC efficacy. The predictive model combining these three features was constructed, and it had an AUC of 0.732 (95% CI: 0.633, 0.831, p<0.01), a sensitivity of 71.2%, and a specificity of 70.7%. The data demonstrate that the orbital MRI features can be used to predict IVC efficiency before RB patients are treated.

Current imaging methods for assessing Graves` orbitopathy activity with particular emphasis on FDG-PET.

The most frequent extrathyroidal Graves' disease manifestation is Graves' orbitopathy (GO). The treatment of GO is determined by its severity and activity. There is currently no reliable, impartial method for assessing it clinically or distinguishing fibrosis from active inflammatory disorders. Today, imaging methods including orbital ultrasound (US), computed tomography (CT), and magnetic resonance imaging (MRI) are frequently employed to show pathological abnormalities in the ocular adnexa of GO patients. In addition, a not widely accepted technique - 99mTc-DTPA SPECT - has some potential to evaluate retrobulbar inflammation in GO patients. However, FDG-PET/CT is possibly superior to other imaging modalities in detecting inflammation in GO and it may be useful in assessing disease activity in case of clinical or serological uncertainty. It might also act as an early indicator of GO development and its aggravation before irreversible tissue alterations take place and may be used in the differential diagnosis of inflammatory disorders of the orbit. However, before FDG-PET/CT could be applied in daily clinical practice, the methodology of GO activity assessment with defined cut-off values for radionuclide concentration - standardized units of value (SUV) have to be established and validated. In addition, the limitations of this technique have to be recognized.

Measuring spin in coalescing binaries of neutron stars that show double precursors

Gamma-ray bursts resulting from binary neutron-star mergers are sometimes preceded by precursor flares. These harbingers can be ignited by quasi-normal modes, excited by orbital resonances, shattering the stellar crust of one of the inspiralling stars up to ≳10 s before coalescence. In the rare case when a system displays two precursors, successive overtones of either interface modes or g modes can be responsible for the overstrainings. Since the free-mode frequencies of these overtones have an almost constant ratio, and the inertial-frame frequencies for rotating stars are shifted relative to static ones, the spin frequency of the flaring component can be constrained as a function of the equation of state, the binary mass ratio, the mode quantum numbers, and the spin-orbit misalignment angle. As a demonstration of the method, we find that the precursors of GRB090510 hint at a spin frequency range of 2 ≲ ν⋆/Hz ≲ 20 for the shattering star if we allow for an arbitrary misalignment angle, assuming ℓ = 2 g modes account for the events.

The First Instrumentally Documented Fall of an Iron Meteorite: Orbit and Possible Origin

A bright fireball observed on 2020 November 7, over Scandinavia, produced the first iron meteorite with a well-determined pre-atmospheric trajectory. We calculated the orbit of this meteoroid and found that it demonstrates no close affinity with the orbit of any known asteroid. We found that the meteoroid (or its parent body) most probably entered the near-Earth orbit from the main asteroid belt via either ν 6 secular resonance with Saturn (89%) or 3:1 mean-motion resonance with Jupiter (11%). The long YORP timescale of the meteoroid suggests that it could have been produced in the main asteroid belt and survived the journey to the near-Earth orbit.

Miopexia supra-ecuatorial del recto lateral en el tratamiento del síndrome «sagging/heavy eye» miópico

PurposeTo describe the outcome of the patients diagnosed of sagging/heavy eye associated to myopia, that were operated on with the supra-equatorial displacement with lateral rectus myopexy. MethodsA retrospective study of 9 cases between 2017 and 2023. The following data were analyzed: horizontal and vertical deviation, diplopia, amblyopia, ductions, ocular torsion, sensorial test, macular pathology, and the orbital magnetic resonance. Treatment was considered successful if the diplopia was improved or eliminated and a final vertical deviation≤5prism diopters (PD). ResultsThe mean age (SD) was: 62.11 (4.6) years (100% women). A total of 88.88% presented diplopia. The mean preoperative hypotropia was: 11.33PD (SD 3.16), and the mean final VD 3.44PD (SD 3.05). After surgery, the hypotropia was overcorrected in one case, under corrected in 5, and orthophoria was achieved in another 3. The technique was associated with surgery of another rectus muscle in 4 subjects. The mean follow-up time after surgery was 34 months (SD 34.62). Six of the 9 patients improved with a vertical deviation≤5PD. In 3 patients, the diplopia was eliminated, while in 5 it remained intermittent (3 with macular pathology). ConclusionSupra-equatorial displacement with lateral rectus myopexy for treatment of myopic sagging/heavy eye is a therapeutic option if hypotropia is less than 12PD or the Yokoyama technique is not indicated. A good result was obtained in most cases, although diplopia could only be totally suppressed in three, and another five remained intermittent.

Primary Sjögren’s syndrome misdiagnosed as Mikulicz’s disease: a case report

BackgroundSjögren’s Syndrome (SS) is an inflammatory autoimmune disease, and Mikulicz’s disease (MD) is a lymphoproliferative disorder. Both MD and SS are more common in middle-aged female, and the dry eyes could be presented in both of them with different degree. The MD patients are characterized by symmetrical swelling of the lacrimal glands which also can occur in the early stage of SS. And the imaging findings between early stage of SS and MD are lack of specificity. Therefore, SS and MD have similarities in the clinical manifestations, imaging and pathological findings and are confused in diagnosis.Case presentationA 51-year-old female patient presented with bilateral swelling of the upper eyelids for 2 years. She also reported having dry mouth and dry eyes which could be tolerated. The Schirmer’s test result is positive and the laboratory tests indicate serum total IgG increased. In the bilateral lacrimal gland area could palpate soft masses. The orbital magnetic resonance imaging (MRI) examination showed bilateral lacrimal gland prolapse. While the histopathological result was considered as MD. The immunohistochemical (IHC) staining results were positive for IgG and negative for IgG4. To clarify the diagnosis, SS-related laboratory tests were performed: anti-SSA antibody (+++), anti-SSB antibody (+++), anti-Ro-52 antibody (+++). With a comprehensive consideration, the final diagnosis was SS.ConclusionWhen the clinical manifestations are atypical, it is necessary to pay attention to the differential diagnosis of SS and MD.

Design of Mars global longitudinal coverage constellation leveraging resonant and periodic orbits in Mars-Phobos-Deimos system

Over the last decades, the exploration of Phobos and Deimos has acquired relevance from both scientific and human missions standpoint. Both moons can play a key role on supporting the Martian Exploration program improving teleoperation capabilities and infrastructure support. The purpose of this work is to propose a different approach to the problem of global longitudinal coverage of Mars, exploiting the characteristic of natural satellites of the planet itself. The proposed constellation can be an alternative to the Mars Areostationary Orbit (MAO), in fact, three satellites equally spaced at Deimos height are enough to provide global longitudinal coverage, with a reduced cost. The main source of perturbation at areostationary height is due to the second degree, second order sectorial harmonic of Mars gravitational field (J2,2), which requires high maintenance cost for an equivalent configuration in MAO. By leveraging Lyapunov orbits in the Mars-Deimos perturbed Three Body Problem, it’s possible to achieve long term stable orbits with lower cost, as well as ballistic orbits with bounded variations. The characteristics and the performance of the constellation are analyzed, as well as the transfer orbits between the Mars-Deimos Lagrange points leveraging resonant orbits. The possibility of placing an extra satellite in an orbit around Phobos with the purpose of increasing performance is also detailed, as well as the transfer trajectory from the Deimos L3 point to a DRO orbit around Phobos.

Discovery and characterization of two Neptune-mass planets orbiting HD 212729 with TESS

ABSTRACT We report the discovery of two exoplanets orbiting around HD 212729 (TOI 1052, TIC 317060587), a Teff = 6146 K star with V = 9.51 observed by TESS in Sectors 1 and 13. One exoplanet, TOI-1052b, is Neptune-mass and transits the star, and an additional planet TOI-1052c is observed in radial velocities but not seen to transit. We confirm the planetary nature of TOI-1052b using precise radial velocity observations from HARPS and determined its parameters in a joint RV and photometry analysis. TOI-1052b has a radius of $2.87^{+0.29}_{-0.24}$ R⊕, a mass of 16.9 ± 1.7 M⊕, and an orbital period of 9.14 d. TOI-1052c does not show any transits in the TESS data, and has a minimum mass of $34.3^{+4.1}_{-3.7}$ M⊕ and an orbital period of 35.8 d, placing it just interior to the 4:1 mean-motion resonance. Both planets are best fit by relatively high but only marginally significant eccentricities of $0.18^{+0.09}_{-0.07}$ for planet b and $0.24^{+0.09}_{-0.08}$ for planet c. We perform a dynamical analysis and internal structure model of the planets as well as deriving stellar parameters and chemical abundances. The mean density of TOI-1052b is $3.9^{+1.7}_{-1.3}$ g cm−3 consistent with an internal structure similar to Neptune. A nearby star is observed in Gaia DR3 with the same distance and proper motion as TOI-1052, at a sky projected separation of $\scriptstyle \sim$1500 au, making this a potential wide binary star system.

Relegation-free closed-form perturbation theory and the domain of secular motions in the restricted three-body problem

We propose a closed-form (i.e., without expansion in the orbital eccentricities) scheme for computations in perturbation theory in the restricted three-body problem (R3BP) when the massless particle is in an orbit exterior to the one of the primary perturber. Starting with a multipole expansion of the barycentric (Jacobi-reduced) Hamiltonian, we carry out a sequence of normalizations in Delaunay variables by Lie series, leading to a secular Hamiltonian model without use of relegation. To this end, we introduce a book-keeping analogous to the one proposed in Cavallari and Efthymiopoulos (Celest Mech Dyn Astron 134(2):1–36, 2022) for test particle orbits interior to the one of the primary perturber, but here adapted, instead, to the case of exterior orbits. We give numerical examples of the performance of the method in both the planar circular and the spatial elliptic restricted three-body problem, for parameters pertinent to the Sun-Jupiter system. In particular, we demonstrate the method’s accuracy in terms of reproducibility of the orbital elements’ variations far from mean-motion resonances. As a basic outcome of the method, we show how, using as criterion the size of the series’ remainder, we reach to obtain an accurate semi-analytical estimate of the boundary (in the space of orbital elements) where the secular Hamiltonian model arrived at after eliminating the particle’s fast degree of freedom provides a valid approximation of the true dynamics.

Confirming Resonance in Three Transiting Systems

Although resonant planets have orbital periods near commensurability, resonance is also dictated by other factors, such as the planets’ eccentricities and masses, and therefore must be confirmed through a study of the system’s dynamics. Here, we perform such a study for five multiplanet systems: Kepler-226, Kepler-254, Kepler-363, Kepler-1542, and K2-32. For each system, we run a suite of N-body simulations that span the full parameter space that is consistent with the constrained orbital and planetary properties. We study the stability of each system and look for resonances based on the libration of the critical resonant angles. We find strong evidence for a two-body resonance in each system; we confirm a 3:2 resonance between Kepler-226c and Kepler-226d, confirm a 3:2 resonance between Kepler-254c and Kepler-254d, and confirm a three-body 1:2:3 resonant chain between the three planets of Kepler-363. We explore the dynamical history of two of these systems and find that these resonances most likely formed without migration. Migration leads to the libration of the three-body resonant angle, but these angles circulate in both Kepler-254 and Kepler-363. Applying our methods to additional near-resonant systems could help us identify which systems are truly resonant or nonresonant and which systems require additional follow-up analysis.