Kinematic Consistency Research Articles

Connecting seismically active normal faults with Quaternary geological structures in a complex extensional environment: The Colfiorito 1997 case history (northern Apennines, Italy)

The northern Apennines of Italy are characterized by a complex Tertiary tectonic history, where superposed compressional and extensional deformation occurred. In such regions, characterized by low active extensional strain rate, the coseismic surface ruptures are rare and often a matter of much debate resulting in a difficult connection between “geological” faults (i.e., faults which can be mapped at the surface) and “seismological” faults (i.e., faults which actually generate earthquakes). The availability of detailed geological mapping and high‐resolution seismological data for the Colfiorito area, struck in 1997 by a sequence of six 5 <Mw≤ 6 normal faulting earthquakes, allow us to compare and verify the existence of geometric and kinematic correspondence between the mapped geological Quaternary faults and the activated structures. In map view, the earthquakes distribution reflects the fault pattern mapped at the surface, the length of activated and mapped faults is quite similar (7–10 km), the coseismic subsided region imaged by interferometric synthetic aperture radar data, is located in the hanging wall of the mapped normal faults that bound the Quaternary basins. In section view, there is a geometric connection between mapped normal faults and the aftershock alignments used to image fault geometry at depth. Comparison of striated fault planes and aftershock focal mechanism solutions show a strong kinematic consistency. This study points out that the Quaternary tectonosedimentary evolution and the present‐day geological and geomorphologic setting of the Colfiorito area can be interpreted as the result of repeated, extensional earthquakes, similar to the 1997 events, occurring on NW‐SE trending normal faults. Our data also show that the main shocks of the Colfiorito sequence nucleated close to the intersections between the normal faults and the preexisting compressional/transpressional structures, which in 1997 acted as lateral barriers to rupture propagation and consequently constrained the fault size.

Kinematic consistency between the Dead Sea Fault Zone and the Neogene and Quaternary left-lateral faulting in SE Turkey

A revised quantitative kinematic model has been determined for the Dead Sea Fault Zone (DSFZ) and the left-lateral fault zones in SE Turkey. The relative motions of the African and Arabian plates across the DSFZ are represented by relative rotation about 31.1°N 26.7°E at 0.40±0.02° Ma −1. The northern DSFZ, in Syria and southern Turkey, is interpreted for the first time as a series of transpressional stepovers, along which the left-lateral slip rate is substantially less than the rate of relative plate motion, because this slip is oblique to the plate motion. The slip rate on the East Anatolian Fault Zone (EAFZ) is estimated as ∼8 mm a −1. Restoring its observed slip thus requires its age to be ∼4 Ma. The previous phase of deformation, which involved slip on the Malatya–Ovacık Fault Zone (MOFZ) before the EAFZ came into being, is thus dated to ∼7–4 Ma, suggesting initiation of the North Anatolian Fault Zone (NAFZ) at ∼7 Ma, not ∼5 Ma as previously thought. The total left-lateral slip on the northern DSFZ in southernmost Turkey is estimated as at least ∼65 km, partitioned with ∼45 km on the Amanos Fault, ∼10 km on the East Hatay Fault, and a further ∼10 km on the Kırkpınar Fault farther east. Much of this slip is inferred to have occurred during the Miocene, before the modern geometry of this plate boundary zone developed. When it first formed, the AF–AR plate boundary was relatively complex—it initially reactivated preexisting structures in the Palmyra foldbelt in Syria and in the Gaziantep region of southern Turkey, which were significantly misaligned relative to the plate motion, requiring major components of shortening as well as left-lateral slip. The transition, from this initial rather diffuse geometry to the present localised geometry of the DSFZ across western Syria, occurred within the Miocene. The predicted rate of relative motion between the stable interiors of the Turkish and African plates in the vicinity of their common boundary onshore of İskenderun Gulf in southern Turkey is estimated as westward at ∼9 mm a −1. However, this “promontory” of the African plate is itself moving westward relative to the stable interior of this plate at ∼7–8 mm a −1. The rate of localised left-lateral slip on the onshore part of this boundary, the NE-trending Yakapınar–Göksun Fault, is thus estimated as only ∼2 mm a −1. This locality can also be regarded as within the distributed boundary zone between the Turkish and Arabian plates. The estimated relative motion between these plates is at ∼8.7 mm a −1 towards the SSW, partitioned between localised left-lateral slip at ∼2 mm a −1 on the Yakapınar–Göksun Fault, and at least ∼1 mm a −1 on the Amanos Fault, and ∼2.5 mm a −1 on East Hatay Fault, with at most distributed left-lateral simple shear at ∼3.2 mm a −1 across the Amanos Mountains in between. However, the combined slip on left-lateral faults east of the Amanos Mountains may be as high as ∼6 mm a −1, with slip at ∼1.7 mm a −1 on the Amanos Fault and at ∼4.3 mm a −1 on the East Hatay Fault and any active faults farther east. This requires no more than ∼0.7 mm a −1 of distributed simple shear across the Amanos Mountains, raising the possibility that this component of deformation may in fact be zero, this small nonzero estimate possibly indicating a closure error arising from minor errors in predicted values of other relative motion vectors. It is proposed that this boundary between the Turkish and African plates first developed at the same time as the MOFZ and NAFZ, but its original geometry involving left-lateral slip on the Karataş–Osmaniye Fault has since become locked by the presence of relatively strong ophiolitic crust within this fault zone. This quantitative kinematic model demonstrates, for the first time, how it is possible for the left-lateral faulting accommodating the NNW–SSE relative motion between the Arabian and African plates in NW Syria to “dovetail” into the left-lateral faulting accommodating the WSW–ENE relative motion between the Turkish and Arabian plates in SE Turkey.

Dynamics of the quasielasticO16(e,e′p)reaction atQ2≈0.8(GeV∕c)2

The physics program in Hall A at Jefferson Lab commenced in the summer of 1997 with a detailed investigation of the ^(16)O(e,e′p) reaction in quasielastic, constant (q,ω) kinematics at Q^2≈0.8(GeV/c)^2, q≈1GeV/c, and ω≈445MeV. Use of a self-calibrating, self-normalizing, thin-film waterfall target enabled a systematically rigorous measurement. Five-fold differential cross-section data for the removal of protons from the 1p-shell have been obtained for 0<p_miss<350MeV/c. Six-fold differential cross-section data for 0<E_miss<120MeV were obtained for 0<p_miss<340MeV/c. These results have been used to extract the ALT asymmetry and the R_L, R_T, R_LT, and R_(L+TT) effective response functions over a large range of E_miss and p_miss. Detailed comparisons of the 1p-shell data with Relativistic Distorted-Wave Impulse Approximation (RDWIA), Relativistic Optical-Model Eikonal Approximation (ROMEA), and Relativistic Multiple-Scattering Glauber Approximation (RMSGA) calculations indicate that two-body currents stemming from meson-exchange currents (MEC) and isobar currents (IC) are not needed to explain the data at this Q^2. Further, dynamical relativistic effects are strongly indicated by the observed structure in ALT at p_miss≈300MeV/c. For 25<E_miss<50MeV and p_miss≈50MeV/c, proton knockout from the 1s1/2-state dominates, and ROMEA calculations do an excellent job of explaining the data. However, as p_miss increases, the single-particle behavior of the reaction is increasingly hidden by more complicated processes, and for 280<p_miss<340MeV/c, ROMEA calculations together with two-body currents stemming from MEC and IC account for the shape and transverse nature of the data, but only about half the magnitude of the measured cross section. For 50<E_miss<120MeV and 145<p_miss<340MeV/c, (e,e′pN) calculations which include the contributions of central and tensor correlations (two-nucleon correlations) together with MEC and IC (two-nucleon currents) account for only about half of the measured cross section. The kinematic consistency of the 1p-shell normalization factors extracted from these data with respect to all available O16(e,e′p) data is also examined in detail. Finally, the Q^2-dependence of the normalization factors is discussed.

Calibration of 5-hole Probe for Flow Angles from Advanced Technologies Testing Aircraft System Flight Data

This paper describes the investigations carried out to calibrate the 5-hole probe for flow angles from advanced technologies testing aircraft system flight data. The flight tests were carried out with gear up and at nominal mid-centre of gravity location for two landing flap positions, *df = IN and 14?. Dynamic manoeuvres were executed to excite the short period and Dutch roll mode of the aircraft. In addition, pull up, push down and steady sideslip manoeuvres were also carried out. The data compatibility check on the recorded flight data has been carried out using maximum likelihood output error algorithm to estimate the bias, scale factor, and time delay in the pressure measurements from the 5-hole probe mounted on a noseboom in front of aircraft nose. Through a way of kinematic consistency checking, flight-validated scale factors, biases, and time delays are determined for the differential pressure measurements for both angle of attack and angle of sideslip. Also, the dynamic pressure measurement is found to have time delays. Based on the earlier investigations, it is once again confirmed that the measurements of attitude angles, obtained from the inertial platform, clearly indicate time delays referred to the other signals like linear accelerations and angular rates which are measured with the dedicated flight instrumentation package. The identified time delays in attitude angles agreed well with the inertial platform specifications. The estimates of sensitivity coefficients and scale factors from the flight data analysis correlates reasonably well with the manufacturer Rosemount calibration curves for the tested Mach range 0.23-0.53. The flight data analysis at Mach number of about 0.59 indicate Mach dependency for the angle of attack.13;

Kinematic Data Consistency in the Inverse Dynamic Analysis of Biomechanical Systems

Inverse dynamic analysis is used in the study ofhuman gait to evaluate the reaction forces transmittedbetween adjacent anatomical segments and to calculate thenet moments-of-force that result from the muscle activityabout each biomechanical joint. The quality of theresults, in terms of reaction and muscle forces, is greatlyaffected not only by the choice of biomechanical model butalso by the kinematic data provided as input. This three-dimensional data is obtained through the reconstruction ofthe measured human motion. A biomechanical model isdeveloped representing human body components with acollection of rigid bodies interconnected by kinematicjoints. The data processing, leading to the spatialreconstruction of the anatomical point coordinates, usesfiltering techniques to eliminate the high frequencycomponents arising from the digitization process. Thetrajectory curves, describing the positions of theanatomical points are obtained using a form of polynomialinterpolation, generally cubic splines. The velocities andaccelerations are then the polynomial derivatives. Thisprocedure alone does not ensure that the kinematic data isconsistent with the biomechanical model adopted, becausethe underlying kinematic constraint equations are notnecessarily satisfied. In the present work, thereconstructed spatial positions of the anatomical pointsare corrected by ensuring that the kinematic constraints ofthe biomechanical model are not violated. The velocity andacceleration equations of the biomechanical model are thencalculated as the first and second time derivatives of theconstraint equations. The solution to these equationsprovides the model with kinematically consistent velocitiesand accelerations. The procedures are demonstrated throughthe application to a normal cadence stride period and theresults discussed with respect to the underlying principlesof the techniques used.

Equatorial Upwelling in the Central Pacific Estimated from Moored Velocity Profilers

Horizontal divergence and vertical velocity (w) are estimated at 0°, 140°W using an array of five subsurface moored acoustic Doppler current profilers deployed from May 1990 to June 1991 during the Tropical Instability Wave Experiment. The record-length mean flow is divergent within the near-surface region and convergent within the thermocline, with maximum convergence located at the high speed core of the Equatorial Undercurrent (EUC). This pattern of divergence results in upwelling at and above the EUC core (with maximum value of 2.3 × 10−5 m s−1 located at 60-m depth) and downwelling below the core. The relative slopes in the zonal plane between the mean velocity vectors and the isotherms suggest a net diffusive heat flux. Assuming that this occurs vertically, an entrainment velocity parameterization provides an estimate of the “diapycnal vertical velocity” profile that reverses sign at the EUC core depth. Several kinematical and dynamical consistency checks are developed on both the time-dependent and the mean motions to supplement a discussion of errors for the mean w profile. The time-dependent fluctuations in w may be an order of magnitude larger than the mean values, and on synoptic timescales w may be directed either up or down over the entire upper 250-m region sampled.

Electromyographic timing analysis of forward and backward cycling

Backward walking to running progressions are becoming a popular, nontraditional component of functional knee rehabilitation programs. The purpose of this electromyographic (EMG) and motion analysis study was to compare the activation duration of the vastus medialis, vastus lateralis, rectus femoris, medial hamstrings, lateral hamstring, tibialis anterior, and gastrocnemius muscles during forward and backward cycling. We hypothesized that the hamstrings would demonstrate greater activation duration during backward cycling. The right lower extremity of 12 healthy subjects (6 male and 6 female) was instrumented with surface EMG electrodes and retroreflective markers to confirm lower extremity kinematic consistency between conditions. Statistical analysis of hip, knee, and ankle kinematics (200 Hz sampling rate) and gender failed to reveal significant differences between conditions (P > 0.05). Quadrant analysis of muscle activation duration with Bonferroni corrections for multiple comparisons revealed that medial and lateral hamstring activation duration was greater during the early recovery phase (quadrant III) of backward cycling than forward cycling (P < 0.00156). Rectus femoris activation duration was greater in the early propulsive phase of backward cycling (quadrant 1) (P < 0.00156) and in the early recovery phase of forward cycling (quadrant III) (P < 0.00156). These findings lend support for the use of backward cycling during the early recovery phase (quadrant III) to achieve a selective hamstring muscle response of relatively decreased patellofemoral stress and anterior cruciate ligament strain.

Mesozoic doming extensional tectonics of Wugongshan, South China

Wugongshan in Jiangxi Province, China was a Mesozoic granitic dome-type extensional tectonics that is composed of metamorphic core complexes, ductile and brittle shear-deformed zones distributed around Mesozoic granites. Within it, the foliation defines an E-W elliptical shape and bears S-N stretching lineations. The axial part is located in Hongjiang-Wanlongshan area and occupied by oriented granites with coaxial symmetric shear fabrics. The southem and northern flanks, including rocks in the Anfu Basin to the south and the Pingxiang Basin to the north, display top-to-south and top-to-north motions, respectively. The ductile and brittle structures indicate a geometric and kinematic consistency. The extensional tectonics is developed on a Caledonian metamorphic basement and is unconformably covered by Late Cretaceous red beds. Isotopic ages on muscovite, biotite and whole rock by40Ar-39Ar, K-Ar and Rb-Sr suggest that the Wugongshan extensional doming began from the Triassic and ended in the Late Cretaceous. A geodynamic model is discussed.

Kinematics of the southern Walker Lane Belt and motion of the Sierra Nevada block, California

Deformation in the southern Walker Lane Belt region of the southwestern Great Basin accommodates significant portions of both Pacific‐North America transform motion and Basin and Range extension. Apparent kinematic inconsistencies between geodetic and fault slip data in this region have made it difficult to understand the nature of the interaction between these deformation processes and to infer the regional kinematics. We model the kinematics of this region in a manner that enforces kinematic consistency and includes fault geometry and slip rate data, Global Positioning System (GPS) survey data, and very long baseline interferometry/very long baseline array (VLBI/VLBA) site velocity data. A model is found that is consistent with the set of available data, and this model differs significantly from prior models for the region. Our model has the Sierra Nevada block, which bounds the western margin of the Great Basin, moving N50°W±5° at 12.7±1.5 mm/yr, with only minor amounts of counterclockwise rotation. Left‐lateral slip on the western Garlock Fault is a consequence of the relatively great westerly component of Sierra Nevada velocity. We also find that the Basin and Range extension east of our study area occurs at a rate of about 2.5 mm/yr, which is slower than the rate in the central Great Basin.

Identification of a nonlinear aerodynamic model of the F-14 aircraft

This effort identified a full subsonic flight envelope model of the aerodynamics of the F-14 aircraft. The data set consisted of 8.9 h of flight data stored as 983 separate maneuver files. The analysis used a unified system identification computer code implementing kinematic consistency, model structure determination, and parameter estimation functions. The code implements generalized filter error, encompassing both equation error and output error types of performance measures. The code can operate in a nearly automated manner, completely processing about 1 h of flight data in about 40 h of Unix workstation time. The resulting aerodynamic model represents nonlinear angle of attack, Mach number, and static flexibility effects. This model has 521 independent aerodynamic terms and 97 independent instrumentation terms. The identified model is an incremental model that adds to an existing nonlinear simulation. One and two dimensional spline functions represent the aerodynamic coefficients.

Equilibrium constrained assumed natural co‐ordinate strain plate elements

AbstractEquilibrium constraints are used to improve the stress accuracy of existing assumed natural‐co‐ordinate strain (ANS) plate elements. This is accomplished by introducing hierarchical degrees of freedom, which are subsequently eliminated by invoking kinematic consistency and element‐interior homogeneous equilibrium conditions. The resulting element enrichments are completely contained in the strain‐displacement matrix. In addition, the modified displacement shape functions become available for consistent mass and nodal load calculations, a feat not shared by some hybrid‐type elements. The performance of the present element (ANS‐EC) is compared with other plate bending elements. This performance comparison includes convergence studies for both displacements and stresses.

Tectonic setting of the Sandia pluton: An orogenic 1.4 Ga granite in New Mexico

Structural studies of the circa 1.42 Ga Sandia pluton and its aureole document significant deformation synchronous with pluton emplacement and call into question the “anorogenic” label associated with this and other 1.4 Ga granites in the southwestern United States. The SE margin of the pluton is a 1‐ to 2‐km‐wide NW dipping ductile shear zone. Field and microstructural observations (melt‐filled shear bands, high‐temperature dynamic recrystallization of K‐feldspar megacrysts, and crosscutting pegmatite dikes) indicate that top‐to‐the‐NW (normal) movement in the shear zone took place in the presence of melt. Subparallel magmatic fabrics north of and structurally above the shear zone contain kinematic indicators consistent with top‐to‐the‐NW shear sense, suggesting that over large regions of the pluton, magmatic flow mimicked solid‐state strain. In the northern aureole, contact metamorphic aluminosilicate porphyroblasts grew during the formation of a NE striking crenulation cleavage (S3) and related folds of late‐stage pegmatite dikes. These features document the synchroneity of magma emplacement, shortening, and metamorphism and indicate that the Sandia pluton is syntectonic, not anorogenic. We interpret the kinematic consistency of structural elements from the base of the pluton, the interior of the pluton, and the northern aureole to reflect a regional (larger than the pluton) strain field and suggest that the “orogeny” recorded in and around the Sandia pluton involved a three dimensional strain field with subhorizontal extension (N–S) and contraction (E–W) directions. N–S extension is documented by the orientation of mineral lineations and movement directions in the basal shear zone and in high‐strain zones in the northern aureole and by the orientations of tabular pegmatite and aplite dikes in the pluton and aureole. East to SE shortening is documented in the northern aureole by orientations of folded pegmatite dikes and associated S3 crenulation cleavage, and east to SE shortening (or least extension) directions in the pluton proper are documented by the intersections of orthogonal dikes. Thus emplacement of the Sandia pluton is interpreted to record a snapshot of regional strains inboard of an active plate margin, rather than local strains generated by emplacement.

Age of deformation within the Central Metasedimentary Belt boundary thrust zone, southwest Grenville Orogen: constraints on the collision of the Mid-Proterozoic Elzevir terrane

U–Pb zircon and titanite geochronology on syntectonic intrusions from the Ontario Central Metasedimentary Belt boundary thrust zone has constrained the timing of two major periods of northwest-directed ductile thrusting on this crustal-scale shear zone. Initiation of deep-seated uppermost amphibolite facies deformation is constrained to a period before 1190 Ma, over 100 Ma earlier than previous estimates. Major reimbrication of the shear zone took place ca. 1080 – 1060 Ma and was more pronounced in the southwestern segment. The initiation of deformation within the boundary thrust zone coincides with the emplacement of the hanging wall Elzevir terrane of the Central Metasedimentary Belt onto the Mid-Proterozoic Laurentian margin. The structural nature and temporal and kinematic consistency of the reimbrication phase along the 200 km exposed length of the shear zone is thought to be due to within-plate reactivation of the existing, rheologically weak structure, a result of continent–continent collision ca. 1080–1060 Ma during the later stage of the Grenville orogenic cycle.Collision of the Elzevir terrane, interpreted to be an ensialic marginal basin, with the Laurentian margin along the Central Metasedimentary Belt boundary thrust zone is thought to potentially record closure of the marginal basin ca. 1190 Ma. A distinctive tonalitic suite of rocks preserved in the boundary thrust zone may be composed of fragments of the remnant arc to the marginal basin.

Inferring feasible assemblies from spatial constraints

The authors treat two different problems in the analysis of assemblies, and algorithms are described for each. The first problem is the selection of consistent sets of part feature relationships, and it corresponds to a search over possible configurations of parts that are consistent with feature set mappings. The second problem is the evaluation of the kinematic consistency of an assembly that has been defined by consistent feature sets. These two problems are linked together as two of the steps required in a search for all correct assembly configurations of a given set of parts. Several of the other necessary steps related to part interference, path feasibility, and workcell device kinematics are referred to but not analyzed. The proposed search algorithm is based on a constraint posting strategy, i.e. rather than generating and testing all specific alternatives, chunks of the search space are progressively removed from consideration by constraints that rule them out until one satisfactory alternative is found.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the constitutive modeling of transient creep in polycrystalline ice

The theoretical generality of constitutive models for the transient creep of polycrystalline ice and the ability of such models to represent knowledge derived from experimentation in a physically consistent manner are examined in this paper. The focus is on physically based but phenomenological models that employ evolving internal state variables to characterize the deformation resistance offered by the material. These include the models of Le Gac and Duval (1980) and Shyam Sunder and Wu (1989a, b). The widely used model of Sinha (1978), though not based on the theory of internal state variables, is also discussed briefly. A set of nine criteria are identified that should be used in evaluating transient-creep models for polycrystalline ice. These include the well-known correspondence between the creep and constant strain-rate responses observed experimentally by Mellor and Cole (1982, 1983) and the ability to reduce creep and constant strain-rate responses into non-dimensional forms that are independent of the loading parameters, viz., temperature and stress or strain rate, as proposed by Ashby and Duval (1985). The kinematic consistency between the response variables during transient creep, i.e., strain, strain rate and time, also emerges as an important consideration in constitutive modeling and the subsequent use of such models in a finite element framework. To satisfy this requirement, the model must accurately predict the experimentally observed relationship between all three pairs of kinematic variables (strain versus time, strain rate versus time, and strain rate versus strain) keeping the material parameters fixed. This paper finds that the formulations of Le Gac and Duval (1980) and Sinha (1978) are unable to satisfy the requirement of kinematic consistency. On the basis of the nine evaluation criteria, the formulation proposed by Shyam Sunder and Wu (1989a) emerges as the more complete creep model for polycrystalline ice. In conclusion, the paper identifies difficult problems that will benefit from future research.

Present-day kinematics of the plate boundary zone between Africa and Europe, from the Azores to the Aegean

Anticlockwise rotation of Africa relative to Europe around an Euler pole in the eastern Atlantic causes plate convergence in the central Mediterranean towards ∼ N20°W at rate considered a priori to be ∼ 5–10 mm yr −1. However, previous summaries of the present-day deformation sense in the central Mediterranean are inconsistent with observations in southern Italy. Recent investigations of Italy and adjacent parts of North Africa enable local deformation sense observed to be reconciled with sense predicted from relative plate motions. Suggested angular velocity of the African plate relative to Europe is ∼ 0.07° Myr −1, around a pole near 21°N, 21°W. This predicts ∼ 2.6 mm yr −1 maximum extension rate towards N64°E near the Azores, consistent with the minimum local accretion of new oceanic crust in the past few millions of years, and ∼ 4.3 mm yr −1 plate convergence towards N20°W in the central Mediterranean at 13°E. Further east, the northern margin of the African plate can be regarded as the Gargano seismic zone in the central Adriatic Sea. The northern Adriatic Sea is a microplate rotating anticlockwise relative to Europe at ∼ 0.3° Myr −1 around a pole in northwestern Italy, causing northeastward shortening in Yugoslavia and up to ∼ 4 mm yr −1 extension in central and northern Italy. The African plate is deforming internally in Tunisia and northern Libya, extending obliquely in direction ∼ E10°S at rate up to ∼ 5.5 mm yr −1. The resultant velocity relative to Europe in the Ionian and southern Adriatic Seas, ∼ 5 mm yr −1 towards ∼ N50°E, explains the observed relative velocity across southern Italy. Kinematic consistency requires present-day shortening rate east of Calabria associated with subduction on the Tyrrhenian Sea Benioff zone and Tyrrhenian Sea extension rate to be both zero or equal to within ∼ 1 mm yr −1.

Screw-matrix method in dynamics of multibody systems

In the present paper the concept of screw in classical mechanics is expressed in matrix form, in order to formulate the dynamical equations of the multibody systems. The mentioned method can retain the advantages of the screw theory and avoid the shortcomings of the dual number notation. Combining the screw-matrix method with the tool of graph theory in Roberson/Wittenberg formalism. We can expand the application of the screw theory to the general case of multibody systems. For a tree system, the dynamical equations for eachj-th subsystem, composed of all the outboard bodies connected byj-th joint can be formulated without the constraint reaction forces in the joints. For a nontree system, the dynamical equations of subsystems and the kinematical consistency conditions of the joints can be derived using the loop matrix. The whole process of calculation is unified in matrix form. A three-segment manipulator is discussed as an example.

Maximum Likelihood Estimation of Parameters in Nonlinear Flight Mechanics Systems

Two methods for maximum likelihood estimation of flight mechanics parameters have been developed. They are applicable to system models which may be nonlinear in the state and control variables as well as in the parameters to be estimated. The optimization problem has been solved by using both minimum search methods and quasi-linearization method. Advantages and disadvantages of both methods are discussed. In the latter case the need for deriving explicit sensitivity equations has been overcome by approximating the sensitivity coefficients by numerical differences. This results in a computationally attractive implementation of the estimation method for routine applications to general nonlinear systems. These techniques have been applied to the problems of kinematic consistency checking of flight test data as well as estimation of aerodynamic derivatives.

Kinematic consistency in ferromagnets with single-ion anisotropy: Application to FeCl2

We have developed a theory which makes the expression for temperature-dependent magnon energies, obtained by means of boson representations of spin operators, kinematically consistent. The theory is applied to FeCl2, a S = 1 ferromagnet with rather large anisotropy, to calculate the temperature dependence of the energy gap of the uniform mode. Both a self-consistently renormalized spin-wave theory and an exact calculation at low temperatures by a T-matrix approach seem to indicate the presence of an anisotropic exchange in addition to easy-axis single-ion anisotropy. Comparison with experimental data shows the fundamental role of the correct treatment of the anisotropy.

Exact low-temperature self-energy of the uniaxial Heisenberg ferromagnet

Dyson (1956) showed that the bosonic approximation in the Hartree-Fock scheme is valid for the isotropic Heisenberg ferromagnet at low temperatures while evident inconsistencies arise if one considers the single-ion anisotropy. For the Heisenberg uniaxial antiferromagnet, a very simple rule D to D(1-1/2S) (where D is the anisotropy strength) was suggested by Rastelli and his co-workers (1974) to restore the kinematical consistency on the basis of the 1/z expansion of repeated scattering processes due to the anisotropy. Balucani and his co-workers (1979) considered the same prescription for the Heisenberg uniaxial ferromagnet and demonstrated that it is true if one takes into account all the contributions proportional to D. The authors have calculated all the contributions in D up to infinite order in the ladder approximation. They find that the exact result is kinematically consistent and agrees with the suggestion of Balucani and his co-workers for small anisotropy but differs from it for strong anisotropy.