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At least 847 records · Page 47

Nonlinear simulation of a flexible aircraft in maneuvering flight

A mathematical model integrating nonlinear rigid-body flight mechanics and linear aeroelastic dynamics is examined; the equations of motion for an elastic aircraft in accelerated flight are developed using Lagrangian mechanics. This approach is used to construct a simulation model of an F/A-18 (configured with tip missiles) which includes angular/elastic inertial coupling (IC). In general, the elastic modes significantly affected by IC were aerodynamically decoupled from the rest of the model. The affected modes were those which induced changes in total aircraft mass distribution. The elastic effect is noticeable if deformation-induced mass distribution changes are significant with respect to modal mass and modal frequencies. A modal parameter is presented which characterizes the level of IC between elastic momentum and rigid-body angular momentum.

Buttrill, Carey S.↗

Existence of tidal tails for the globular cluster NGC 5824

Context: Several dynamically cold streams have been associated with certain globular clusters (GCs) based on orbital energies and angular momenta. Some of these streams are surprisingly far apart from their progenitors and one such pair is Triangulum and NGC 5824. Triangulum can be considered as a piece of the leading tail of NGC 5824 since the cluster’s future orbit matches well with the stream’s track. The existence of the leading tail of NGC 5824 is the motivation behind the search for its trailing tail. Aims: Our goal is to confirm the connection between Triangulum and NGC 5824. We also search for the trailing tail of the cluster. Methods: The selection of member stars of Triangulum is made through various cuts in metallicity, proper motions (PMs), radial velocity and a color–magnitude diagram (CMD). The selected members are compared in phase space to a mock stream that models the disruption of NGC 5824. We then try to detect the trailing tail of the cluster based on a modified matched-filter technique. Stars are assigned weights using their color differences from the cluster’s locus in the CMD. These weights are further scaled, based on the stars’ departures from expected PMs of the model stream. Results: A total of 26 member stars for Triangulum are obtained, 16 of which are newly identified. These members are consistent with the mock stream in the phase space, and their metalicity and position on the CMD are in good agreement with NGC 5824. By applying the matched filter, a tenuous trailing tail of the cluster is detected, spanning ~50° long on sky. The signature matches well with the mock stream’s trajectory. Conclusions: Our results support that the Triangulum stream acts as a part of the leading tail for NGC 5824. On the trailing side, we detected a 50° tail extending from the cluster. The existence of both leading and trailing tails for the GC NGC 5824 is verified.

79 ASTRONOMY AND ASTROPHYSICS↗

Manual for a workstation-based generic flight simulation program (LaRCsim), version 1.4

LaRCsim is a set of ANSI C routines that implement a full set of equations of motion for a rigid-body aircraft in atmospheric and low-earth orbital flight, suitable for pilot-in-the-loop simulations on a workstation-class computer. All six rigid-body degrees of freedom are modeled. The modules provided include calculations of the typical aircraft rigid-body simulation variables, earth geodesy, gravity and atmospheric models, and support several data recording options. Features/limitations of the current version include English units of measure, a 1962 atmosphere model in cubic spline function lookup form, ranging from sea level to 75,000 feet, rotating oblate spheroidal earth model, with aircraft C.G. coordinates in both geocentric and geodetic axes. Angular integrations are done using quaternion state variables Vehicle X-Z symmetry is assumed.

Jackson, E. Bruce↗

Orion Handling Qualities During ISS Rendezvous and Docking

The Orion spacecraft was designed to rendezvous with multiple vehicles in low earth orbit (LEO) and beyond. To perform the required rendezvous and docking task, Orion must provide enough control authority to perform coarse translational maneuvers while maintaining precision to perform the delicate docking corrections. While Orion has autonomous docking capabilities, it is expected that final approach and docking operations with the International Space Station (ISS) will initially be performed in a manual mode. A series of evaluations was conducted by NASA and Lockheed Martin at the Johnson Space Center to determine the handling qualities (HQ) of the Orion spacecraft during different docking and rendezvous conditions using the Cooper-Harper scale. This paper will address the specifics of the handling qualities methodology, vehicle configuration, scenarios flown, data collection tools, and subject ratings and comments. The initial Orion HQ assessment examined Orion docking to the ISS. This scenario demonstrates the Translational Hand Controller (THC) handling qualities of Orion. During this initial assessment, two different scenarios were evaluated. The first was a nominal docking approach to a stable ISS, with Orion initializing with relative position dispersions and a closing rate of approximately 0.1 ft/sec. The second docking scenario was identical to the first, except the attitude motion of the ISS was modeled to simulate a stress case ( 1 degree deadband per axis and 0.01 deg/sec rate deadband per axis). For both scenarios, subjects started each run on final approach at a docking port-to-port range of 20 ft. Subjects used the THC in pulse mode with cues from the docking camera image, window views, and range and range rate data displayed on the Orion display units. As in the actual design, the attitude of the Orion vehicle was held by the automated flight control system at 0.5 degree deadband per axis. Several error sources were modeled including Reaction Control System (RCS) jet angular and position misalignment, RCS thrust magnitude uncertainty, RCS jet force direction uncertainty due to self plume impingement, and Orion center of mass uncertainty.

Hart, Jeremy J.↗

Stabilization of gaze during circular locomotion in darkness. II. Contribution of velocity storage to compensatory eye and head nystagmus in the running monkey

1. Yaw eye in head (Eh) and head on body velocities (Hb) were measured in two monkeys that ran around the perimeter of a circular platform in darkness. The platform was stationary or could be counterrotated to reduce body velocity in space (Bs) while increasing gait velocity on the platform (Bp). The animals were also rotated while seated in a primate chair at eccentric locations to provide linear and angular accelerations similar to those experienced while running. 2. Both animals had head and eye nystagmus while running in darkness during which slow phase gaze velocity on the body (Gb) partially compensated for body velocity in space (Bs). The eyes, driven by the vestibuloocular reflex (VOR), supplied high-frequency characteristics, bringing Gb up to compensatory levels at the beginning and end of the slow phases. The head provided substantial gaze compensation during the slow phases, probably through the vestibulocollic reflex (VCR). Synchronous eye and head quick phases moved gaze in the direction of running. Head movements occurred consistently only when animals were running. This indicates that active body and limb motion may be essential for inducing the head-eye gaze synergy. 3. Gaze compensation was good when running in both directions in one animal and in one direction in the other animal. The animals had long VOR time constants in these directions. The VOR time constant was short to one side in one animal, and it had poor gaze compensation in this direction. Postlocomotory nystagmus was weaker after running in directions with a long VOR time constant than when the animals were passively rotated in darkness. We infer that velocity storage in the vestibular system had been activated to produce continuous Eh and Hb during running and to counteract postrotatory afterresponses. 4. Continuous compensatory gaze nystagmus was not produced by passive eccentric rotation with the head stabilized or free. This indicates that an aspect of active locomotion, most likely somatosensory feedback, was responsible for activating velocity storage. 5. Nystagmus was compared when an animal ran in darkness and in light. the beat frequency of eye and head nystagmus was lower, and the quick phases were larger in darkness. The duration of head and eye quick phases covaried. Eye quick phases were larger when animals ran in darkness than when they were passively rotated. The maximum velocity and duration of eye quick phases were the same in both conditions. 6. The platform was counterrotated under one monkey in darkness while it ran in the direction of its long vestibular time constant.(ABSTRACT TRUNCATED AT 400 WORDS).

NASA Discipline Neuroscience↗

Two-electron interference in two-photon attosecond double ionization of neon

The pump-probe experiments enabled by x-ray free-electron lasers (XFEL) will allow us to directly observe correlated electronic motion with attosecond time resolution by detecting photoelectron pairs in coincidence. In helium, the transition between the nonsequential and sequential regime in two-photon double ionization (TPDI) is well explained by a virtual-sequential model. Much less is known, however, about the TPDI process in more complex atoms. Recently, we extended the virtual-sequential model to arbitrary light pulses [Chattopadhyay Phys. Rev. A 108, 013114 (2023)]. This extension employs multichannel scattering states for the single ionization of both the neutral and the ionized target, which we initially applied to helium. In the present study, we show that our extended virtual-sequential model reproduces the qualitative features of the angularly integrated observables with available experimental results for neon, a considerably more complex target. We observe an intriguing feature of inverted two-particle interference in the joint-energy distribution of Ne compared to He. Finally, this phenomenon, attributable to the presence of a final doubly ionized state with triplet symmetry coupled to the two photoelectrons, should be observable with current experimental technologies.

74 ATOMIC AND MOLECULAR PHYSICS↗

Orbital-induced crossover of the Fulde-Ferrell-Larkin-Ovchinnikov phase into Abrikosov-like states.

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state can emerge in superconductors for which the orbital critical field exceeds the Pauli limit. Here, we present angular-resolved specific-heat data of the quasi-two-dimensional organic superconductor ??-(ET)2Cu(NCS )2 , with a focus on high fields in the regime of the FFLO transition. For an increasing out-of-plane tilt of the applied magnetic field, which leads to an increase of orbital contributions, we found that the nature of the superconducting transition changes from second to first order and that a further transition appears within the high-field superconducting phase. However, the superconducting state above the Pauli limit is stable for field tilt of several degrees. Since any finite perpendicular component of the magnetic field necessarily leads to quantization of the orbital motion, the resulting vortex lattice states compete with the modulated order parameter of the FFLO state leading to complex high-field superconducting phases. By solving the linearized self-consistency equation within weak-coupling BCS theory, we show that our results are clear experimental evidence of an orbital-induced transformation of the FFLO order parameter into Abrikosov-like states of higher Landau levels.

Kotte, Tommy↗

Hydrodynamic Stability and Magnetic Reconnection in Disks and Stars

The purpose of this grant is to study parametric instability. The simplest example of parametric instability is a harmonic oscillator with a periodic modulation of the spring constant. If the modulation frequency is close to twice the natural frequency of the oscillator, the amplitude of oscillation tends to grow exponentially. The growth rate is proportional to the strength of the modulation, but it also depends upon the closeness to resonance of the two frequencies, and upon natural damping rate or "Q" of the oscillator. Parametric instabilities are very common in physics. A familiar example is a jogger's ponytail--normally a very strongly damped pendulum, it can be destabilized by the variation in effective gravity during the jogger's stride. Observation confirms that the period of the pendulum is half that of the jogger's vertical motion. In astrophysics, parametric instability may occur by external tidal forcing, or by interaction among eigenmodes. In the latter case, an energetic eigenmode may destabilize modes of half its frequency, provided some weak nonlinearity exists to couple them. Under a previous Astrophysical Theory grant (NAGW-2419), the PI discovered a parametric instability of tidally forced disks such as the accretion disks in cataclysmic variables and X ray binaries [2]. The destabilized modes are tightly-wound, incompressible, three-dimensional waves analogous to g-modes and r-modes in stars. Later work has confirmed our analysis [4]. It was hoped that these modes might provide a source of turbulence and angular momentum transport in accretion disks. However, a follow-up investigation of this instability by local numerical simulations, although confirming the analytically estimated growth rates, found negligible angular momentum flux [3]. Other work, partly supported by the ATP, now strongly indicates that the transport mechanism in such disks is magnetohydrodynamic turbulence [6]. Nevertheless, the parametric mechanism may truncate the outer edges of disks in close binaries [2], and it may be important in disks of very low ionization such as protostellar disks, or even cataclysmic-variable disks in quiescence where the MHD mechanism may be ineffective [5]. All analyses up to 1996 were done in a local approximation where the orbital frequency, shear rate, and tidal field were treated as constants. The locally computed growth rate turns out to depend strongly on radius, and it was unclear how to average these local rates to obtain the correct global rate. This is a critical issue for accretion disks in close binaries, because the local growth rate is comparable to the orbital frequency towards the outer edge of the disk but decreases rapidly inwards. Paper #1 examined this issue in a simplified global model where the destabilizing terms vary with position. We found that the global growth rate is essentially equal to the maximum local rate, provided that the latter is smoothed over a radial range equal to the distance that the destabilized wave propagates at its group speed in one growth time. Thus, in an accretion disk, waves would grow rapidly in the outer parts but would propagate both inwards and outwards at a maximum group speed of order the disk thickness divided by the orbital period.

Goodman, Jeremy↗

Method of Obtaining High Resolution Intrinsic Wire Boom Damping Parameters for Multi-Body Dynamics Simulations

The goal of NASA's Magnetospheric MultiScale (MMS) mission is to understand magnetic reconnection with sensor measurements from four spinning satellites flown in a tight tetrahedron formation. Four of the six electric field sensors on each satellite are located at the end of 60- meter wire booms to increase measurement sensitivity in the spin plane and to minimize motion coupling from perturbations on the main body. A propulsion burn however, might induce boom oscillations that could impact science measurements if oscillations do not damp to values on the order of 0.1 degree in a timely fashion. Large damping time constants could also adversely affect flight dynamics and attitude control performance. In this paper, we will discuss the implementation of a high resolution method for calculating the boom's intrinsic damping, which was used in multi-body dynamics simulations. In summary, experimental data was obtained with a scaled-down boom, which was suspended as a pendulum in vacuum. Optical techniques were designed to accurately measure the natural decay of angular position and subsequently, data processing algorithms resulted in excellent spatial and temporal resolutions. This method was repeated in a parametric study for various lengths, root tensions and vacuum levels. For all data sets, regression models for damping were applied, including: nonlinear viscous, frequency-independent hysteretic, coulomb and some combination of them. Our data analysis and dynamics models have shown that the intrinsic damping for the baseline boom is insufficient, thereby forcing project management to explore mitigation strategies.

Yew, Alvin G.↗

Motion of trapped electrons and protons in Saturn's inner magnetosphere

A summary is given of basic formulas for the guiding center motion of energetic charged particles trapped in a dipolar magnetic field. These formulas for longitudinal drift rates, latitudinal bounce periods, equatorial gyroradii, and equatorial gyroperiods are then stated in convenient numerical form for electrons and protons as functions of kinetic energy E, magnetic shell parameter L, and equatorial pitch angle alpha 0 for a slightly simplified model of the observed magnetic field of Saturn. To aid in the study of the interaction of charged particles with the rings and inner satellites of Saturn, additional formulas are given for the time interval between successive encounters of charged particles with a satellite in a circular prograde orbit and for the energy of electrons whose longitudinal angular velocity is resonant, or synchronous, with the Keplerian angular velocity of such a satellite.

Thomsen, M. F.↗

Large scale structure in universes dominated by cold dark matter

The theory of Gaussian random density field peaks is applied to a numerical study of the large-scale structure developing from adiabatic fluctuations in models of biased galaxy formation in universes with Omega = 1, h = 0.5 dominated by cold dark matter (CDM). The angular anisotropy of the cross-correlation function demonstrates that the far-field regions of cluster-scale peaks are asymmetric, as recent observations indicate. These regions will generate pancakes or filaments upon collapse. One-dimensional singularities in the large-scale bulk flow should arise in these CDM models, appearing as pancakes in position space. They are too rare to explain the CfA bubble walls, but pancakes that are just turning around now are sufficiently abundant and would appear to be thin walls normal to the line of sight in redshift space. Large scale streaming velocities are significantly smaller than recent observations indicate. To explain the reported 700 km/s coherent motions, mass must be significantly more clustered than galaxies with a biasing factor of less than 0.4 and a nonlinear redshift at cluster scales greater than one for both massive neutrino and cold models.

Bond, J. Richard↗

Advances in Estimation of the Earth Orientation Parameters From Observation

Historically, a two-step procedure for estimation of Universal Time and polar motion from observations was adopted: night averages from individual observatories formed a raw non-equidistant time series that was edited for outliers, smoothed, and formed the final data product. This approach was by inertia used for processing modern space geodesy observations. I will present an alternative one-step approach and its application for processing a dataset of VLBI observations since 1990.0 through present. The essence of this approach is to represent the Earth orientation parameters in a form of an expansion into basic functions and estimate of the expansion coefficients directly from observations. A further extension of this approach is to assimilate not only space geodesy data, but atmospheric and ocean angular momentum from assimilation numerical weather models and their forecasts. That makes a smooth bridge between Earth rotation estimation and prediction. I will talk about my experience of running data analysis in such a way on a semi-operational basis, present results, and discuss advantages and disadvantages of this approach.

Leonid Petrov↗

High Resolution VLBA Observations of NGC 4261

The VLBA's high angular resolution at 22 and 43 GHz allows the nuclei of nearby radio galaxies to be imaged with very high linear resolution (a few hundred Schwarzschild radii or less for central black hole masses of about 10(exp 8) - 10(exp 9) solar mass). This is the scale on which absorption by the dense ionized inner regions of nuclear accretion disk should be detected. We present 8, 22, and 43 GHz VLBA images of the two-sided radio jets in NGC 4261 (2C370) with sub-parsec resolution, and derive constraints on the physical properties of the inner accretion disk. In addition, preliminary results from multi-epoch VLBA observations to detect proper motions in the jet and counterjet, and thus determine the orientation of the radio axis to our line of sight, may be available. Our multi-frequency images show apparent absorption by a nearly edge-on disk at 8 GHz, but not evidence for absorption at 22 or 43 GHz. Assuming that this is due to a lower optical depth for free-free absorption at 22 and 43 GHz, we find an upper limit for the electron density of approximately 10(exp 8)* Square root of(0.1/L)/cubic cm, where L is the path length through the disk in pc. The disk inclination, and therefore the likely path length, will be better determined by the ongoing VLBA proper motions measurements. This research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

Jones, D. L.↗

A Deep HRI Survey of Low-Mass PMS Stars in NGC 2264

Brian Patten is the Principal Investigator of the NASA ADP project 'A Deep HRI Survey of Low-Mass PMS Stars in NGC 2264'. This project was funded to support primarily the data reduction and analysis for new ROSAT data to be acquired in ROSAT AO8. For AO8 we were awarded two deep (100 ks) exposures with the ROSAT HRI instrument of a rotation and proper-motion selected sample of young (3 Myr - 15 Myr), low-mass, PMS stars in the populous star-forming region NGC 2264. These X-ray data were to be combined with an extensive rotation database for members of this cluster to allow us, for the first time, to probe the early evolution of magnetic dynamo activity for both fully convective stars and those stars found lower on the Hayashi tracks which have developed radiative cores. This database would have been used to study the interrelationship between coronal activity level, interior structure, and rotation rate as a function of mass and age.in the PMS and to define empirical constraints for theoretical models of angular momentum and magnetic dynamo evolution.

Patten, Brian↗

Mineralogical, Elemental, and Tomographic Reconnaissance Investigation for CLPS (METRIC)

METRIC is a robotic science laboratory that can determine the mineralogy, elemental chemistry, micromorphology, and thermophysical properties of planetary regolith. The METRIC suite comprises METRIC XRD/F, an X-ray diffraction/X-ray fluorescence instrument that can determine the mineralogy and elemental chemistry of regolith samples; METRIC XCT, a micro X-ray computed tomography instrument that can be used to evaluate grain/crystallite sizes and textures; METRIC IRS, an imaging spectrometer mounted on a rover that can determine mineralogy and thermophysical properties at the landing site; and a pneumatic sample collection, processing, distribution system developed by Honeybee Robotics. The payload elements could be deployed on a static lander or a rover. Data returned from the METRIC payload would inform origin, formation, and evolution of rocky planetary bodies. METRIC XRD/F draws on heritage from the CheMin instrument on the Mars Science Laboratory (MSL) Curiosity rover [1], with a few important improvements. Like CheMin, METRIC XRD/F operates in transmission geometry and uses piezoelectric actuators on sample cells in a tuning fork geometry to induce convective grain motion of the regolith to create a randomly oriented powder. MSL CheMin uses an energy-sensitive CCD to collect XRD patterns and XRF spectra simultaneously from the same sample cell, resulting in qualitative XRF data. METRIC XRD/F uses two different sample cells, one optimized for XRD and one optimized for XRF, and a silicon drift detector to detect fluoresced X-rays. This improvement to the XRF capabilities provides quantitative geochemical data of major elements down to Z = 11 and allows for the detection of minor and trace elements that are critical for evaluating geologic evolution of the Moon (e.g., P and Th). Modest improvements to the XRD geometry and hardware allow for better angular resolution and the ability to distinguish between members of the pyroxene group. METRIC XCT uses the same geometry and much of the same hardware as METRIC XRD/F, where a CCD would capture images of a regolith sample in a 3 mm diameter sample tube that is rotated 360° in steps <1°. Image brightness can be used to infer compositional data, where brighter materials indicate a higher Z, much like scanning electron microscopy. Data from METRIC XCT complement those from METRIC XRD/F. Particle size, shape, and texture can provide petrologic and provenance information, whereas vesicle size and morphology in volcanic or impact melt lithologies can inform cooling rates. METRIC IRS is a hyperspectral thermal imager that can be mounted to a lander or rover to provide mineralogical data from the broader landing site and help determine whether the samples analyzed by METRIC XRD/F and XCT are representative. The METRIC IRS spectral range (8–14 μm) and resolution (10.8 cm-1) allow for quantitative mineralogy from modelling Reststrahlen bands of major rock-forming minerals (e.g., silicates, phosphates). Radiance cubes can be processed and modelled with an onboard high-performance computer to determine mineral abundances of plagioclase, high-Ca pyroxene, pigeonite, orthopyroxene, olivine, and glass. Regolith samples can be acquired, processed, and delivered to the X-ray instruments via multiple sample handling systems, but the pneumatic sampling systems developed by Honeybee Robotics [e.g., 2] are best suited for relatively low-cost missions that are being competed for the Moon (e.g., NASA’s Payloads and Research Investigations for the Surface of the Moon program). There are pneumatic sampling systems that collect surface material and other systems that pneumatically drill up to ~1 m below the surface, providing material that has not been space weathered and has not been affected by the lander’s exhaust. [1] Blake, D. F., Vaniman, D., Achilles, C., Anderson, R., Bish, D., et al. (2012). Space Sci. Rev. 170, 341-478. https://doi.org/10.1007/s11214-012-9905-1. [2] Zacny, K., Betts, B., Hedlund, M., Long, P., Gramlich, M., Tura, K., Chu, P., Jacob, A., Garcia, A. (2014). IEEE Aerospace Conference, 3-7 March 2014, Big Sky, MT, U.S.A.

X-ray diffraction↗

Singular perturbation equations for flexible satellites

Force equations of motion of the individual flexible elements of a satellite were obtained in a previous paper. Moment equations of motion of the composite bodies of a flexible satellite are to be developed using two sets of equations which form the basic system for any dynamic model of flexible satellites. This basic system consists of a set of N-coupled, nonlinear, ordinary, or partial differential equations, for a flexible satellite with n generalized, structural position coordinates. For single composite body satellites, N is equal to (n + 3); for dual-spin systems, N is equal to (n + 9). These equations involve time derivatives up to the second order. The study shows a method of avoiding this linearization by reducing the N equations to 3 or 9 nonlinear, coupled, first order, ordinary, differential equations involving only the angular velocities of the composite bodies. The solutions for these angular velocities lead to linear equations in the n generalized structural position coordinates, which can be solved by known methods.

Huang, T. C.↗

Aeromechanical stability of helicopters with a bearingless main rotor. Part 1: Equations of motion

Equations of motion for a coupled rotor-body system were derived for the purpose of studying air and ground resonance characteristics of helicopters that have bearingless main rotors. For the fuselage, only four rigid body degrees of freedom are considered; longitudinal and lateral translations, pitch, and roll. The rotor is assumed to consist of three or more rigid blades. Each blade is joined to the hub by means of a flexible beam segment (flexbeam or strap). Pitch change is accomplished by twisting the flexbeam with the pitch-control system, the characteristics of which are variable. Thus, the analysis is capable of implicitly treating aeroelastic couplings generated by the flexbeam elastic deflections, the pitch-control system, and the angular offsets of the blade and flexbeam. The linearized equations are written in the nonrotating system retaining only the cyclic rotor modes; thus, they comprise a system of homogeneous ordinary differential equations with constant coefficients. All contributions to the linearized perturbation equations from inertia, gravity, quasi-steady aerodynamics, and the flexbeam equilibrium deflections are retained exactly.

Hodges, D. H.↗

A Deep X-Ray Survey of Low Mass PMS Stars in NGC 2264

We have proposed to make a deep X-ray survey of a rotation- and proper-motion selected sample of young (3-15 Myr old), low-mass, pre-main sequence (PMS) stars in the populous star-forming region NGC 2264. These X-ray Multimirror Mission (XMM) data will be combined with an extensive set of rotation data for members of this cluster to allow us, for the first time, to probe the early evolution of magnetic dynamo activity for both fully convective stars and those stars found lower on their Hayashi tracks, which are developing radiative cores. We will use these data to study the interrelationship between rotation, interior structure, and coronal activity as a function of mass and age in the PMS and to define empirical constraints for theoretical models of angular momentum/dynamo evolution.

Patten, Brian M.↗