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At least 865 records · Page 48
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

National User Resource for Biological Accelerator Mass Spectrometry (Final Report)

The National User Resource for Biological Accelerator Mass Spectrometry (User Resource) will provide isotopic analysis (primarily radiocarbon or 14C) by accelerator mass spectrometry (AMS) for NIH- funded researchers across the United States and will be the only User Resource of its type in the United States. The User Resource will provide measurement capability and expertise to a research community that requires highly sensitive, quantitative isotope analyses. Since commissioning a new accelerator mass spectrometer in June 2014, we have measured over 4000 samples a year for collaborators and service users. The User Resource will enable us to continue to meet these research needs, as well as provide for new users whose research programs would benefit from AMS as a measurement tool. The User Resource’s forte will be ultra-high sensitivity quantitation of radiocarbon and selected other radioisotopes for research studies where isotopes are required. Radioisotope labeling studies have been and will continue to be an important tool for addressing many complex biomedical science problems. AMS is a specialized and unique type of mass spectrometry that provides absolute quantitation of radiocarbon and other relevant radioisotopes with extreme sensitivity, having limits of detection in real samples on the order of a few attomol/mg of sample at measurement precisions of ~3%. It is the only instrumental method capable of quantifying radioisotope-labeled agents routinely in real-world samples with such precision and sensitivity. The sensitivity of AMS allows for the quantification of radiolabeled metabolites in extremely complex matrices of cells and organisms at very low concentrations and in small samples. AMS allows studies to be conducted without perturbing metabolism leading to more relevant quantification of metabolic rates and pathways. In addition, it enables quantification of pharmacokinetic and metabolic properties of toxicants at environmentally relevant concentrations in model systems as well as the ability to quantify pharmacokinetics and other molecular endpoints directly in humans. Such quantitative assessments can 1) improve risk assessment for toxicants, 2) address safety and efficacy considerations for therapeutic entities, 3) deepen understanding of xenobiotic and intermediary metabolism, 4) help understand the interactions between critical molecular pathways, and 5) improve efforts to model and predict various metabolic and biological states. These capabilities have been applied in a number of areas including research in carcinogenesis, toxicology, nutrition, pharmacology/drug development and basic biological science. As a NIGMS National Resource the National User Resource for Biological Accelerator Mass Spectrometry will help NIH funded scientists achieve a deeper understanding of the etiology of human health concerns by (1) enabling the quantification of pharmacokinetics and other molecular endpoints directly in humans; (2) offering the ability to conduct quantitative studies using biologics such as proteins or lipids, and thereby reducing the amount of radioisotope usage in biomedical labs; and (3) enabling more relevant studies of metabolic pathways in health and disease through the use of much lower, more biologically-relevant, concentrations of metabolic substrates in cells and intact organisms. Such studies support NIGMS’s basic biomedical research areas that contribute to the understanding of fundamental cellular and physiological principles and enable research supported by the Biophysics, Biomedical Technology, and Computational Biosciences (BBCB); Genetics and Molecular, Cellular, and Developmental Biology (GMCDB); Pharmacology, Physiology, Biological Chemistry (PPBC) and Training, Workforce Development, and Diversity (TWD) Divisions. Over the next five years, our goals are to: 1. Improve the efficiency of operation for AMS measurements through installation of new interfaces to our AMS systems, technical modifications to improve gas accepting ion source efficiency and upgrading our data analysis software for improved ease of use and data reporting. 2. Increase the accessibility and visibility of ultra-sensitive 14C measurements for the biomedical research community by training of new investigators and expanding our national user base. 3. Provide high throughput, ultra-sensitive 14C analysis for the NIGMS and NIH user community.

47 OTHER INSTRUMENTATION↗
DOE OSTI2026

The Kinetic-Energy–Momentum–Mass 5-Flux of a Baryon Fluid in Bargmann Spacetimes

A Bargmann spacetime is a constrained five-dimensional setting that, while introducing no new physical degrees of freedom beyond those of ordinary four-dimensional spacetime, permits Galilei physics to be expressed with a tensor formalism that respects the distinction between mass and energy while affording the conceptual and technical advantages of a spacetime metric. This framework offers a route to a strong-field ‘Galilei general relativity’ approximating the usual Poincaré general relativity introduced by Einstein. In preparation for modeling core-collapse supernovae, where such an approximation would be useful, this work generalizes the kinetic-energy–momentum–mass 5-flux 𝒯 and its associated spacetime tensor law from a simple fluid of constant particle mass to a baryon fluid whose multiple nuclear species can interconvert rest mass and internal energy. The spacetime tensor law on Bargmann–Galilei spacetime 𝐵𝒢 and its decompositions relative to comoving (‘Lagrangian’) and fiducial (‘Eulerian’) observers are derived in detail. The formalism is rendered more suitable for core-collapse supernova modeling by an extension from strict 𝐵𝒢 to a regime that might be denoted as 𝐵𝒢+: microscopically Poincaré yet macroscopically Galilei. This extension accommodates energy generation by nuclear composition changes and allows comoving energy density and pressure to contribute relative to mass density, while preserving the simplifications of Galilei bulk fluid flow and the streamlined geometry governed by the Bargmann–Galilei spacetime metric.

Cardall, Christian [ORNL] (ORCID:000000020086105X)↗
DOE OSTI2021

TOI-954 b and K2-329 b: Short-period Saturn-mass Planets that Test whether Irradiation Leads to Inflation

We report the discovery of two short-period Saturn-mass planets, one transiting the G subgiant TOI-954 (TIC 44792534, V = 10.343, T = 9.78) observed in TESS sectors 4 and 5 and one transiting the G dwarf K2-329 (EPIC 246193072, V = 12.70, K = 10.67) observed in K2 campaigns 12 and 19. We confirm and characterize these two planets with a variety of ground-based archival and follow-up observations, including photometry, reconnaissance spectroscopy, precise radial velocity, and high-resolution imaging. Combining all available data, we find that TOI-954 b has a radius of 0.852{sub −0.062}{sup +0.053} R{sub J} and a mass of 0.174{sub −0.017}{sup +0.018} M {sub J} and is in a 3.68 day orbit, while K2-329 b has a radius of 0.774{sub −0.024}{sup +0.026} R{sub J} and a mass of 0.260{sub −0.022}{sup +0.020} M {sub J} and is in a 12.46 day orbit. As TOI-954 b is 30 times more irradiated than K2-329 b but more or less the same size, these two planets provide an opportunity to test whether irradiation leads to inflation of Saturn-mass planets and contribute to future comparative studies that explore Saturn-mass planets at contrasting points in their lifetimes.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

The Binary INformation from Open Clusters Using SEDs (BINOCS) Project: Reliable Photometric Mass Determinations of Binary Star Systems in Clusters

We introduce a new binary detection technique, Binary INformation from Open Clusters using SEDs (binocs), which we show is able to determine reliable stellar multiplicity and masses over a much larger mass range than current approaches. This new technique determines accurate component masses of binary and single systems of the open clusters’ main sequence by comparing observed magnitudes from multiple photometric filters to synthetic star spectral energy distributions (SEDs), allowing us to systematically probe the binary population for low-mass stars in clusters for eight well-studied open clusters. We provide new deep, infrared photometric catalogs (1.2–8.0 μm) for the key open clusters NGC 1960 (M36), NGC 2099 (M37), NGC 2420, and NGC 2682 (M67), using observations from NOAO/NEWFIRM and Spitzer/IRAC. Using these deep multiwavelength catalogs, the binocs method is applied to these clusters to determine accurate component masses for unresolved cluster binaries. We explore binary fractions as a function of cluster age, Galactic location, and metallicity.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

An Asymmetric Dust Ring around a Very Low Mass Star ZZ Tau IRS

We present Atacama Large Millimeter/submillimeter Array (ALMA) gas and dust observations at band 7 (339 GHz: 0.89 mm) of the protoplanetary disk around a very low mass star ZZ Tau IRS with a spatial resolution of 025. The {sup 12}CO J = 3 → 2 position–velocity diagram suggests a dynamical mass of ZZ Tau IRS of ∼0.1–0.3 M {sub ☉}. The disk has a total flux density of 273.9 mJy, corresponding to an estimated mass of 24–50 M {sub ⊕} in dust. The dust emission map shows a ring at r = 58 au and an azimuthal asymmetry at r = 45 au with a position angle of 135°. The properties of the asymmetry, including radial width, aspect ratio, contrast, and contribution to the total flux, were found to be similar to the asymmetries around intermediate mass stars (∼2 M {sub ☉}) such as MWC 758 and IRS 48. This implies that the asymmetry in the ZZ Tau IRS disk shares a similar origin with others, despite the star being ∼10 times less massive. Our observations also suggest that the inner and outer parts of the disk may be misaligned. Overall, the ZZ Tau IRS disk shows evidence of giant planet formation on a ∼10 au scale at a few megayears. If confirmed, it will challenge existing core accretion models in which such planets have been predicted to be extremely hard to form around very low mass stars.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Characterizing the X-Ray Emission of Intermediate-mass Pre-main-sequence Stars

We use X-ray and infrared observations to study the properties of three classes of young stars in the Carina Nebula: intermediate-mass (2–5 M {sub ⊙}) pre-main-sequence stars (IMPS; i.e., intermediate-mass T Tauri stars), late-B and A stars on the zero-age main sequence (AB), and lower-mass T Tauri stars (TTS). We divide our sources among these three subclassifications and further identify disk-bearing young stellar objects versus diskless sources with no detectable infrared (IR) excess emission using IR (1–8 μm) spectral energy distribution modeling. We then perform X-ray spectral fitting to determine the hydrogen-absorbing column density (N {sub H}), absorption-corrected X-ray luminosity (L {sub X}), and coronal plasma temperature (kT) for each source. We find that the X-ray spectra of both IMPS and TTS are characterized by similar kT and N {sub H}, and on average L {sub X}/L {sub bol} ~ 4 × 10{sup -4}. IMPS are systematically more luminous in X-rays (by ~0.3 dex) than all other subclassifications, with median L {sub X} = 2.5 × 10{sup 31} erg s{sup -1}, while AB stars of similar masses have X-ray emission consistent with TTS companions. These lines of evidence converge on a magnetocoronal flaring source for IMPS X-ray emission, a scaled-up version of the TTS emission mechanism. IMPS therefore provide powerful probes of isochronal ages for the first ~10 Myr in the evolution of a massive stellar population, because their intrinsic, coronal X-ray emission decays rapidly after they commence evolving along radiative tracks. We suggest that the most luminous (in both X-rays and IR) IMPS could be used to place empirical constraints on the location of the intermediate-mass stellar birth line.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

K2-79b and K2-222b: Mass Measurements of Two Small Exoplanets with Periods beyond 10 days that Overlap with Periodic Magnetic Activity Signals

We present mass and radius measurements of K2-79b and K2-222b, two transiting exoplanets orbiting active G-type stars observed with HARPS-N and K2. Their respective 10.99 day and 15.39 day orbital periods fall near periods of signals induced by stellar magnetic activity. The two signals might therefore interfere and lead to an inaccurate estimate of exoplanet mass. We present a method to mitigate these effects when radial velocity (RV) and activityindicator observations are available over multiple observing seasons and the orbital period of the exoplanet is known. We perform correlation and periodogram analyses on subsets composed of each target's two observing seasons, in addition to the full data sets. For both targets, these analyses reveal an optimal season with little to no interference at the orbital period of the known exoplanet. We make a confident mass detection of each exoplanet by confirming agreement between fits to the full RV set and the optimal season. For K2-79b, we measure a mass of 11.8 ± 3.6 M ⊕ and a radius of 4.09 ± 0.17 R ⊕ . For K2-222b, we measure a mass of 8.0 ± 1.8 M ⊕ and a radius of 2.35 ± 0.08 R ⊕ . According to model predictions, K2-79b is a highly irradiated Uranus analog and K2-222b hosts significant amounts of water ice. We also present a RV solution for a candidate second companion orbiting K2-222 at 147.5 days.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Chemical Analysis of the Ultrafaint Dwarf Galaxy Grus II. Signature of High-mass Stellar Nucleosynthesis

We present a detailed abundance analysis of the three brightest member stars at the top of the giant branch of the ultrafaint dwarf (UFD) galaxy Grus II. All stars exhibit a higher than expected [Mg/Ca] ratio compared to metal-poor stars in other UFD galaxies and in the Milky Way (MW) halo. Nucleosynthesis in high-mass ( 20 M ⊙) core-collapse supernovae has been shown to create this signature. The abundances of this small sample (three) stars suggests the chemical enrichment of Grus II could have occurred through substantial high-mass stellar evolution, and is consistent with the framework of a top-heavy initial mass function. However, with only three stars it cannot be ruled out that the abundance pattern is the result of a stochastic chemical enrichment at early times in the galaxy. The most metal-rich of the three stars also possesses a small enhancement in rapid neutron-capture (r-process) elements. The abundance pattern of the r-process elements in this star matches the scaled r-process pattern of the solar system and r-process enhanced stars in other dwarf galaxies and in the MW halo, hinting at a common origin for these elements across a range of environments. All current proposed astrophysical sites of r-process element production are associated with high-mass stars, thus the possible top-heavy initial mass function of Grus II would increase the likelihood of any of these events occurring. The time delay between the α and r-process element enrichment of the galaxy favors a neutron star merger as the origin of the r-process elements in Grus II.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

The Mira-Titan Universe. III. Emulation of the Halo Mass Function

We construct an emulator for the halo mass function over group and cluster mass scales for a range of cosmologies, including the effects of dynamical dark energy and massive neutrinos. The emulator is based on the recently completed Mira-Titan Universe suite of cosmological N-body simulations. The main set of simulations spans 111 cosmological models with 2.1 Gpc boxes. We extract halo catalogs in the redshift range z = [0.0, 2.0] and for masses M-200c >= 10(13)M(circle dot)/h. The emulator covers an eight-dimensional hypercube spanned by {Omega(m)h(2), Omega(b)h(2), Omega(nu)h(2), sigma(8), h, n(s), w(0), w(a)}; spatial flatness is assumed. We obtain smooth halo mass functions by fitting piecewise second-order polynomials to the halo catalogs and employ Gaussian process regression to construct the emulator while keeping track of the statistical noise in the input halo catalogs and uncertainties in the regression process. For redshifts z less than or similar to 1, the typical emulator precision is better than 2% for 10(13)-10(14)M(circle dot)/h and <10<^> M similar or equal to 101(circle dot)(54)/h. For comparison, fitting functions using the traditional universal form for the halo mass function can be biased at up to 30% at M similar or equal to 10(144)M(circle dot)/h for z = 0. Our emulator is publicly available at https://github.com/SebastianBocquet/MiraTitanHMFemulator.

cosmology: theory↗
DOE OSTI2021

The Last Journey. II. SMACC—Subhalo Mass-loss Analysis Using Core Catalogs

Here we introduce Subhalo Mass-loss Analysis using Core Catalogs (SMACC). SMACC adds a mass model to substructure merger trees based on halo "core tracking." Our approach avoids the need for running expensive subhalo finding algorithms and instead uses subhalo mass-loss modeling to assign masses to halo cores. We present details of the SMACC methodology and demonstrate its excellent performance in describing halo substructure and its evolution. Validation of the approach is carried out using cosmological simulations at significantly different resolutions. We apply SMACC to the 1.24-trillion-particle Last Journey simulation and construct core catalogs with the additional mass information. These catalogs can be readily used as input to semianalytic models or subhalo abundance matching approaches to determine approximate galaxy distributions, as well as for in-depth studies of small-scale structure evolution.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Near-infrared Supernova Ia Distances: Host Galaxy Extinction and Mass-step Corrections Revisited

We present optical and near-infrared (NIR, Y-, J-, H-band) observations of 42 Type Ia supernovae (SNe Ia) discovered by the untargeted intermediate Palomar Transient Factory survey. This new data set covers a broad range of redshifts and host galaxy stellar masses, compared to previous SN Ia efforts in the NIR. We construct a sample, using also literature data at optical and NIR wavelengths, to examine claimed correlations between the host stellar masses and the Hubble diagram residuals. The SN magnitudes are corrected for host galaxy extinction using either a global total-to-selective extinction ratio, R V = 2.0, for all SNe, or a best-fit R V for each SN individually. Unlike previous studies that were based on a narrower range in host stellar mass, we do not find evidence for a "mass step," between the color- and stretch-corrected peak J and H magnitudes for galaxies below and above $\mathrm{log}({M}_{* }/{M}_{\odot })=10$. However, the mass step remains significant (3σ) at optical wavelengths (g, r, i) when using a global R V , but vanishes when each SN is corrected using their individual best-fit R V . Our study confirms the benefits of the NIR SN Ia distance estimates, as these are largely exempted from the empirical corrections dominating the systematic uncertainties in the optical.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

The Effect of Supernova Convection On Neutron Star and Black Hole Masses

Abstract Our understanding of the convective-engine paradigm driving core-collapse supernovae has been used for two decades to predict the remnant mass distribution from stellar collapse. These predictions improve as our understanding of this engine increases. In this paper, we review our current understanding of convection (in particular, the growth rate of convection) in stellar collapse and study its effect on the remnant mass distribution. We show how the depth of the mass gap between neutron stars and black holes can help probe this convective growth. We include a study of the effects of stochasticity in both the stellar structure and the convective seeds caused by stellar burning. We study the role of rotation and its effect on the pair-instability mass gap. Under the paradigm limiting stellar rotation to those stars in tight binaries, we determine the effect of rotation on the remnant mass distribution.

Fryer, Chris L. (ORCID:0000000326240056)↗
DOE OSTI2024

Measuring the Conditional Luminosity and Stellar Mass Functions of Galaxies by Combining the Dark Energy Spectroscopic Instrument Legacy Imaging Surveys Data Release 9, Survey Validation 3, and Year 1 Data

In this investigation, we leverage the combination of the Dark Energy Spectroscopic Instrument (DESI) Legacy Imaging Surveys Data Release 9, Survey Validation 3, and Year 1 data sets to estimate the conditional luminosity functions and conditional stellar mass functions (CLFs and CSMFs) of galaxies across various halo mass bins and redshift ranges. To support our analysis, we utilize a realistic DESI mock galaxy redshift survey (MGRS) generated from a high-resolution Jiutian simulation. An extended halo-based group finder is applied to both MGRS catalogs and DESI observation. By comparing the r- and z-band luminosity functions (LFs) and stellar mass functions (SMFs) derived using both photometric and spectroscopic data, we quantified the impact of photometric redshift (photo-z) errors on the galaxy LFs and SMFs, especially in the low-redshift bin at the low-luminosity/mass end. By conducting prior evaluations of the group finder using MGRS, we successfully obtain a set of CLF and CSMF measurements from observational data. We find that at low redshift, the faint-end slopes of CLFs and CSMFs below ~10 9 h –2 L ⊙ (or h –2 M ⊙ ) evince a compelling concordance with the subhalo mass functions. After correcting the cosmic variance effect of our local Universe following Chen et al., the faint-end slopes of the LFs/SMFs turn out to also be in good agreement with the slope of the halo mass function.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

The SAGA Survey. III. A Census of 101 Satellite Systems around Milky Way–mass Galaxies

We present Data Release 3 (DR3) of the Satellites Around Galactic Analogs (SAGA) Survey, a spectroscopic survey characterizing satellite galaxies around Milky Way (MW)-mass galaxies. The SAGA Survey DR3 includes 378 satellites identified across 101 MW-mass systems in the distance range of 25–40.75 Mpc, and an accompanying redshift catalog of background galaxies (including about 46,000 taken by SAGA) in the SAGA footprint of 84.7 deg 2 . The number of confirmed satellites per system ranges from zero to 13, in the stellar mass range of 10 6−10 M ⊙ . Based on a detailed completeness model, this sample accounts for 94% of the true satellite population down to M ⋆ = 10 7.5 M ⊙ . We find that the mass of the most massive satellite in SAGA systems is the strongest predictor of satellite abundance; one-third of the SAGA systems contain LMC-mass satellites, and they tend to have more satellites than the MW. The SAGA satellite radial distribution is less concentrated than the MW's, and the SAGA quenched fraction below 10 8.5 M ⊙ is lower than the MW's, but in both cases, the MW is within 1σ of SAGA system-to-system scatter. SAGA satellites do not exhibit a clear corotating signal as has been suggested in the MW/M31 satellite systems. Although the MW differs in many respects from the typical SAGA system, these differences can be reconciled if the MW is an older, slightly less massive host with a recently accreted LMC/SMC system.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

A measurement of the Higgs boson mass in the diphoton decay channel in proton-proton collisions at $\sqrt{s}$ = 13 TeV

A measurement of the Higgs boson mass in the diphoton decay channel is performed using proton-proton collision data at a center-of-mass energy of 13 TeV. The data set recorded with the CMS detector between 2016 and 2018 is used, corresponding to an integrated luminosity of 138 fb$^{-1}$. A refined detector calibration and new analysis techniques are employed to improve the precision of the results compared to earlier measurements. The Higgs boson mass is measured to be $m_\mathrm{H}$ = 125.13 $\pm$ 0.15 GeV = 125.13 $\pm$ 0.10 (stat) $\pm$ 0.12 (syst) GeV. In addition, a combination with the mass measurement at center-of-mass energies of 7 and 8 TeV in the diphoton final state is performed resulting in $m_\mathrm{H}$ = 125.06 $\pm$ 0.14 GeV = 125.06 $\pm$ 0.09 (stat) $\pm$ 0.11 (syst) GeV.

FOS: Physical sciences↗
DOE OSTI2021

Mass and density of individual frozen hydrometeors

A new precipitation sensor, the Differential Emissivity Imaging Disdrometer (DEID), is used to provide the first continuous measurements of the mass, diameter, and density of individual hydrometeors. The DEID consists of an infrared camera pointed at a heated aluminum plate. It exploits the contrasting thermal emissivity of water and metal to determine individual particle mass by assuming that energy is conserved during the transfer of heat from the plate to the particle during evaporation. Particle density is determined from a combination of particle mass and morphology. A Multi-Angle Snowflake Camera (MASC) was deployed alongside the DEID to provide refined imagery of particle size and shape. Broad consistency is found between derived mass–diameter and density–diameter relationships and those obtained in prior studies. However, DEID measurements show a generally weaker dependence with size for hydrometeor density and a stronger dependence for aggregate snowflake mass.

47 OTHER INSTRUMENTATION↗
NASA NTRS1964

Stellar evolution. ii. the hydrogen-burning phase of a star of 7.0 solar masses <sternentwicklung. ii. die wasserstoff- brennende phase eines sterns von 7.0 sonnenmassen<

With the computer program by Hofmeister, Kippenhahn, Weigert (1964, from now on referred to as ''I") the evolution of a population I star of 7.0 solar masses has been followed. The results presented here are based on a sequence of 119 models, the first of which represents the homogeneous main sequence state and has a convective core containing 26% of the mass. The following models describe the phase of depletion of hydrogen in the core, which is shrinking in mass until the convection around the centre disappears. After this the gradual development of a hydrogen burning shell source is shown. The models show the evolution into the red giant region, while the helium core is contracting until helium burning starts at the centre and a new convective core is built up. The luminousity is increased about 1 magnitude compared with the main sequence state. At the same time the outer convective region grows in mass and covers at the maxi­mum 71% of the total mass of the star. During the evolution to the red giant state, the evolutionary track crosses the region of the cepheids. Some aspects of the corresponding models are discussed.

STELLAR EVOLUTION↗
NASA NTRS1972

Dynamic characteristics of a two-stage variable-mass flexible missile with internal flow

A general formulation of the dynamical problems associated with powered flight of a two stage flexible, variable-mass missile with internal flow, discrete masses, and aerodynamic forces is presented. The formulation comprises six ordinary differential equations for the rigid body motion, 3n ordinary differential equations for the n discrete masses and three partial differential equations with the appropriate boundary conditions for the elastic motion. This set of equations is modified to represent a single stage flexible, variable-mass missile with internal flow and aerodynamic forces. The rigid-body motion consists then of three translations and three rotations, whereas the elastic motion is defined by one longitudinal and two flexural displacements, the latter about two orthogonal transverse axes. The differential equations are nonlinear and, in addition, they possess time-dependent coefficients due to the mass variation.

Meirovitch, L.↗