Kinematic Corrections Research Articles

A method of determining the kinematic properties of the primary mirror elements of the RATAN-600 radio telescope using modern laser measuring systems

We review the methods of determining the alignment errors of the primary mirror and flat reflector elements of the RATAN-600 radio telescope using a modern coordinate measuring system based on the Leica absolute tracker AT402. We computed the kinematic corrections for the elevation drives. The accuracy of the measurement method was estimated. The antenna readout with the introduced kinematic corrections was tested.

Relativistic effects in heavy-ion Coulomb scattering

The role of relativistic corrections in Coulomb scattering of heavy ions at intermediate energy collisions ($E_{lab}\gtrsim 50$ MeV/n) is investigated by numerically solving a full set of coupled equations. We compare two methods, (a) one involving an exact account of interaction retardation with (b) a method based on the expansion of effective Lagrangians in powers of the ion velocities, $v/c$.Our study makes it possible to infer the relevance of kinematic corrections, retardation, and magnetic interactions such as the Darwin force. We show that analytical formulas are able to describe all aspects of experimental interest in relativistic effects in heavy-ion Coulomb scattering at intermediate energies without having to solve numerically the coupled equations.

Nonlinear Thermoelectroelastic Analysis of III-N Semiconductor Devices

The diffusion-drift electron transport description is combined with finite deformation theory to model thermoelectroelastic behaviors in piezoelectric semiconductors under conditions when the mechanical strains/displacements are not small so that the usual assumption of linearity cannot be justified. The nonlinear treatment includes both kinematic and constitutive corrections as well as a proper treatment of the electrostatic conditions at free surfaces. The theory is illustrated using numerical simulations of various III-N devices of technological interest, including of conventional AlGaN/GaN HEMTs and of semiconducting microelectromechanical structures that can require the nonlinear theory’s rotational invariance even when the strains are small. Despite uncertainties in the values of the various material coefficients, it seems likely that the nonlinear corrections are often substantial.

Short-term Impact of Anterior Cruciate Ligament Reconstruction in an Adolescent Population on 3D Knee Kinematics

Objectives:Gait analysis is a proven method for assessing knee biomechanical adaptations in anterior cruciate ligament deficient (ACLD) patients and to quantify the impact of the reconstructive surgery (ACLR). In an adult population, ACLR has shown partial kinematic correction, as they remain in internal tibial rotation, putting them at risk of rotational instability and develop osteoartitis. ACLD adolescents likely adopt similar gait changes to reduce knee instability, but may show quicker or more return to the normal compared to adults. The purpose of this study is to compare the tridimensional (3D) knee kinematics before and after ACLR in adolescents.Methods:25 ACLD patients aged between 13 and 19 years old on a waiting list for ACLR were recruited. Bilateral knee 3D kinematic data was gathered during treadmill walking at comfortable self-selected speed using the KneeKGTM System before and 6-9 months after ACLR. Each participant underwent the same surgical protocol (2-strand hamstring tendon graft, hamstring harvest proximally and kept distally, transphyseal tibial tunnel and transepiphyseal femoral tunnel) by the same experienced surgeon. Three analyses were done: ACLD knee pre vs. post-surgery, contralateral healthy knee pre vs. post-surgery, and ACLR knee vs. healthy contralateral knee.Results:In the sagittal and transverse planes, kinematic patterns remained similar to the pre-op; maintaining the characteristic knee flexion gait pattern during single support phase which is well documented in adult ACLD (hamstring facilitation strategy). The ACLR knee exhibited a more valgus dynamic alignment compared to pre-surgery throughout the gait cycle. The healthy contralateral knee kinematics displayed no significant changes in the frontal and sagittal planes after surgery compared to the pre-op pattern. In the transverse plane, post-op gait analysis showed significantly more external rotation at heel-strike and through weight acceptance. While looking at the gait symmetry post-surgery, ACLR knee revealed significantly more valgus while remaining in greater flexion during single limb support. In the transverse plane, an external rotation tendency is observed in the ACLR knee throughout the gait cycle, except during weight acceptance.Conclusion:This study shows that kinematic adaptations found in ACLD adolescents are likely to endure short term after surgery. For example, the greater knee flexion gait pattern used before surgery is still used after ACLR. Interestingly, adolescents used an external tibial rotation adaptation to limit internal tibial instability before the surgery and this pattern was still present post-surgery. Even if theses protection strategies are efficient, the increased dynamical valgus movement seen could place the graft under pressure while increasing patellofemoral stresses, a common complaint after ACLR. Lastly, post-surgery, the contralateral knee seems to mimic the external tibial rotation gait pattern strategy seen in ACL-knee. This study demonstrates that gait protective strategies are still present short term after the surgery. Biomechanical assessment helps ID these adaptations to optimize post-op rehabilitation and prevent secondary injuries.

Research on presice point positioning and Real-Time Kinematics corrections for unmanned aerial vehicle global positioning systems

Unmanned Aerial Vehicles (UAVs) are used in different tasks with different flight path accuracy. To achieve a greater accuracy of flight trajectory GPS accuracy improvement methods are analyzed. The present article explains the main principles of GPS measurement. Precise Point Positioning (PPP) and Real-Time Kinematics (RTK) methods are described. and compared. Also, both methods have been tested.

Problem of kinematic mass corrections for unpolarized semi-inclusive deep inelastic scattering

Miraculously, target mass corrections for inclusive deep inelastic scattering can be calculated exactly. On the contrary, there does not exist a consistent derivation of kinematic hadron mass corrections for semi-inclusive deep inelastic scattering (SIDIS). Recently this has become of topical interest, since there is a significant difference between the measured HERMES and COMPASS pion and kaon multiplicities, which cannot be explained as a consequence of evolution in $Q^2$, and it has been suggested that the difference can be understood if kinematic hadron mass corrections are taken into account. We explain why this argument is incorrect.

A useful analytical formula to avoid thermal damage in the adaptive control of dry surface grinding

An adaptive control is proposed for dry surface grinding to extend the use of the wheel without needing to be dressed, preserving at the same time the surface integrity of the workpiece. The implementation of this adaptive control needs to use predictive models of thermal damage, as in the case of Malkin's model, which calculates the allowable grinding power before the workpiece gets burnt for any working condition. In this latter case, the adaptive control of the cutting depth condition requires solving a quartic equation. Since the analytical procedures for solving quartics given in the literature are quite cumbersome to implement in the numeric control of the grinding machine, we propose a closed analytic formula in order to compute directly the unique positive solution. Moreover, we can enhance Malkin's model in order to consider an arbitrary heat flux profile entering into the workpiece and the kinematical correction to the geometrical contact length, in such a way that we can still using the latter solution to the quartic equation.

Gravitational deflection of light and massive particles by a moving Kerr–Newman black hole

The gravitational deflection of test particles including light, due to a radially moving Kerr–Newman (KN) black hole with an arbitrary constant velocity that is perpendicular to its angular momentum, is investigated. In harmonic coordinates, we derive the second post-Minkowskian (2PM) equations of motion for test particles, and solve them by high-accuracy numerical calculations. We then concentrate on discussing the kinematical corrections caused by the motion of the gravitational source to second-order deflection. The analytical formula of the light-deflection angle up to the second order by a moving lens is obtained. For a massive particle moving with a relativistic velocity, there are two different analytical results for the Schwarzschild deflection angle up to the second order reported in the previous works, i.e. and , where and w are the mass of the lens, the impact parameter, and the particle’s initial velocity, respectively. Our numerical result is in perfect agreement with the former result. Furthermore, the analytical formula for massive particle deflection up to the second order in the Kerr geometry is achieved. Finally, the possibilities of detecting the motion effects on the second-order deflection are also analyzed.

Linear vs non-linear QCD evolution in the neutrino-nucleon cross section

Evidence for an extraterrestrial flux of ultra-high-energy neutrinos, in the order of PeV, has opened a new era in Neutrino Astronomy. An essential ingredient for the determination of neutrino fluxes from the number of observed events is the precise knowledge of the neutrino-nucleon cross section. In this work, based on [1], we present a quantitative study of σ νN in the neutrino energy range 10 4 E ν 14 GeV within two transversal QCD approaches: NLO DGLAP evolution using different sets of PDFs and BK small- x evolution with running coupling and kinematical corrections. Further, we translate this theoretical uncertainty into upper bounds for the ultra-high-energy neutrino flux for different experiments.

Evaluating corrections for a horizontal offset between sensor and position data for surveys on land

When regarding evolutions in land-based, motorized sensor data collection it can be generalized that the speed of surveying, sampling rates, digital communications speed and survey resolutions have increased over the last years. Possibilities for accurate positioning have been following pace. However, a spatial offset between sensor and position data can be necessary to avoid interference with the instrument or can be the result of using a sensor array. It can also be due to practical considerations such as mounting possibilities. Unfortunately a severe degradation of positional accuracy is possible when performing corrections for a spatial offset and quantification of the induced error is quite difficult. As a consequence, the actual positional accuracy of sensor measurements is therefore often omitted or unknown, and a correction may be neglected during data processing. In this paper, accounting for a horizontal (spatial) offset is researched by examining the use of several correction methods. To evaluate the degree of loss of positional accuracy and validate several correction procedures, global navigation satellite system (GNSS) data (with real-time kinematic correction) have been simultaneously collected, using a GNSS receiver that was mounted on an all-terrain vehicle and two other receivers that were mounted near the front and end of an elongated sensor sled. The sled was connected to the towing vehicle using a flexible connection. Since the positioning systems’ horizontal accuracies were about 20 mm, it was possible to quantify the horizontal error of the predicted positions for the different correction procedures considered. The best approach for high-resolution surveys, which make use of a connection to a cart or sled that can rotate around a pivot on the towing vehicle, was researched. The strengths and weaknesses of the applied corrections were also evaluated, allowing selection of an appropriate correction for a given survey implementation.

Three-body model for the analysis of quasifree scattering reactions in inverse kinematics

A new method to calculate cross sections for $(p,pn)$ and $(p,2p)$ reactions measured under inverse kinematics conditions is proposed. The method uses the prior form of the scattering transition amplitude and replaces the exact three-body wave function appearing in this expression with an expansion in terms of $p\ensuremath{-}n$ or $p\ensuremath{-}p$ states, covering the physically relevant excitation energies and partial waves. A procedure of discretization, similar to that used in continuum-discretized coupled-channels calculations, is applied to make this expansion finite and numerically tractable. The proposed formalism is nonrelativistic, but several relativistic kinematical corrections are applied to extend its applicability to energies of current interest. The underlying optical potentials for the entrance and exit channels are generated microscopically by folding an effective density-dependent $G$ matrix with the density of the composite nucleus. Numerical calculations for $^{12}\mathrm{C}$($p,2p$), $^{12}\mathrm{C}$($p,pn$), and $^{23}\mathrm{O}$($p,pn$) at $\ensuremath{\sim}400$ MeV/nucleon are presented to illustrate the method. The role of final-state interactions and Pauli principle between the outgoing nucleons is also discussed.

PROPER MOTION AND TIMING OF TWO UNUSUAL PULSARS: CALVERA AND 1E 1207.4—5209

Using pairs of images from the Chandra High-Resolution Camera we examine the proper motion of the central compact object (CCO) 1E 1207.4-5209 in the supernova remnant (SNR) PKS 1209-51/52, and the unusual pulsar Calvera that is possibly a CCO descendant. For 1E 1207.4-5209, an insignificant proper motion of 15+/-7 mas/yr is measured, corresponding to a corrected tangential velocity of <180 km/s at the distance of 2 kpc. This proves that the previously noted large offset of the pulsar from the apparent geometric center of the SNR is not due to high proper motion; evidently the symmetry of the remnant does not indicate its center of expansion. Calvera has a marginally significant proper motion of 69+/-26 mas/yr, corresponding to 86+/-33 km/s for a hypothetical distance of 0.3 kpc. Notably, its vector is away from the Galactic plane, although its high Galactic latitude of b = +37 deg may be more a consequence of its proximity than its velocity. We also provide updated timing solutions for each pulsar. Spanning 14.5 yr, the ephemeris of 1E 1207.4-5209 has a small and steady frequency derivative that, because of the negligible proper motion, requires no kinematic correction. The derived surface dipole magnetic field strength of 1E 1207.4-5209 thus remains B_s = 9.8e10 G. Calvera has B_s = 4.4e11 G, intermediate between those of ordinary young pulsars and CCOs, suggesting that it may be on a trajectory of field growth that could account for the absence of descendants in the neighborhood of CCOs in the P-Pdot diagram.

Wide angle Compton scattering on the proton: study of power suppressed corrections

We study the wide angle Compton scattering process on a proton within the soft-collinear factorization (SCET) framework. The main purpose of this work is to estimate the effect due to certain power suppressed corrections. We consider all possible kinematical power corrections and also include the subleading amplitudes describing the scattering with nucleon helicity flip. Under certain assumptions we present a leading-order factorization formula for these amplitudes which includes the hard- and soft-spectator contributions. We apply the formalism and perform a phenomenological analysis of the cross section and asymmetries in the wide angle Compton scattering on a proton. We assume that in the relevant kinematical region where $$-t,-u>2.5$$ GeV $$^{2}$$ the dominant contribution is provided by the soft-spectator mechanism. The hard coefficient functions of the corresponding SCET operators are taken in the leading-order approximation. The analysis of existing cross section data shows that the contribution of the helicity-flip amplitudes to this observable is quite small and comparable with other expected theoretical uncertainties. We also show predictions for double polarization observables for which experimental information exists.

Neutrino-nucleon cross section at ultrahigh energy and its astrophysical implications

We present a quantitative study of the $\nu N$ cross section in the neutrino energy range $10^4<E_{\nu}<10^{14}$ GeV within two transversal QCD approaches: NLO DGLAP evolution using different sets of PDFs and BK small-$x$ evolution with running coupling and kinematical corrections. We show that the non-linear effects embodied in the BK equation yield a slower raise in the cross section for $E_{\nu}\gtrsim 10^{8}$ GeV than the usual DGLAP based calculation. Finally, we translate this theoretical uncertainty into upper bounds for the ultra-high-energy neutrino flux for different experiments.

A note on the Sagnac effect for matter beams

We study the Sagnac effect for matter beams, in order to estimate the kinematic corrections to the basic formula, deriving from the position and the extent of the interferometer, and discuss the analogy with the Aharonov-Bohm effect. We show that the formula for the Sagnac time delay is the same for matter and light beams in arbitrary stationary space-times, provided that a suitable condition on the speed of the beams is fulfilled. Hence, the same results obtained for light beams apply to matter beams.

Inverse kinematics and geometric singularity analysis of a 3-SPS/S redundant motion mechanism using conformal geometric algebra

We propose a 3-SPS/S redundant motion mechanism with kinematic redundancy in this paper. The proposed mechanism with redundancy enables redundant motion as it works like pan/tilt systems to reduce the unnecessary degree of freedom for the yaw and pitch motions in the configuration space. By reducing one degree of freedom, this robot has self-motion that causes the inverse kinematics to have infinite solutions, so that the proposed research performs an optimization process for obtaining the optimal solution using geometric approaches. This optimal solution provides the fastest response among the infinite solutions by minimizing each link movement to the target orientation. In addition, we perform a geometric singularity analysis due to limited link length and avoidance using conformal geometric algebra for the feasibility and correctness of the inverse kinematics.

Kinematic corrections to quarkonium production in the nonrelativistic QCD approach

We present an attempt to explicitly estimate the effect of soft gluon radiation in the nonrelativistic QCD scheme. We stress that the energy of the emitted final state gluons is bounded from below by the confinement scale, and this leads to non-negligible changes in the final state kinematics.

Digital Hardware Realization of Forward and Inverse Kinematics for a Five-Axis Articulated Robot Arm

When robot arm performs a motion control, it needs to calculate a complicated algorithm of forward and inverse kinematics which consumes much CPU time and certainty slows down the motion speed of robot arm. Therefore, to solve this issue, the development of a hardware realization of forward and inverse kinematics for an articulated robot arm is investigated. In this paper, the formulation of the forward and inverse kinematics for a five-axis articulated robot arm is derived firstly. Then, the computations algorithm and its hardware implementation are described. Further, very high speed integrated circuits hardware description language (VHDL) is applied to describe the overall hardware behavior of forward and inverse kinematics. Additionally, finite state machine (FSM) is applied for reducing the hardware resource usage. Finally, for verifying the correctness of forward and inverse kinematics for the five-axis articulated robot arm, a cosimulation work is constructed by ModelSim and Simulink. The hardware of the forward and inverse kinematics is run by ModelSim and a test bench which generates stimulus to ModelSim and displays the output response is taken in Simulink. Under this design, the forward and inverse kinematics algorithms can be completed within one microsecond.

The Inverse Kinematics and Simulation of a Novel 3-DOF Parallel Mechanism

A novel 3-DOF parallel mechanism is presented and the inverse kinematics is derived by using geometric constraint between each rods. The co-simulation based on ADAMS is proceeded to verify the correctness of the inverse kinematics. This algorithm is the basis for the application of such parallel mechanism.

Kinematic cycle slip detection and correction for carrier phase based navigation applications in urban environment in case of ultra high rate GNSS observations

In recent years, GNSS has been more and more widely used for all kinds of applications, including those in urban environment. Carrier phase observations from GNSS are necessary for precise navigation applications. However, before that, cycle slip has to be detected and corrected. For static GPS observations, as the distance between the receiver and the GPS satellites is smooth, the testing quantities formed with carrier phase observations between satellites can be used for cycle slip detection and correction. These testing quantities have two advantages. First, as only carrier phase observations are used, they are not affected by big noise of code observations. Second, the wavelength of the testing quantities is about 20 cm, long enough to be insensitive to carrier phase noise and multipath. However, generally these testing quantities cannot be used for kinematic observations with a sample interval of 1 s as the moving of the receiver and the distance between the receiver and the satellites is not smooth. Kinematic cycle slip detection and correction has been a challenge for many years. Currently, two methods are popularly used: geometry-free and time relative. Both of these two methods are sensitive to observation noise and multipath of carrier phase and code, especially the latter one. For carrier phase based applications in urban environment, this weakness will become more outstanding. For kinematic ultra high rate observations, the changes of the speed and acceleration of the receiver can be neglected in very short time such as 1 s or less if there is no abrupt movement. In this case, the distance between the receiver and the satellites can be regarded as smooth and the testing quantities formed between satellites can be used for cycle slip detection and correction. Based on this, in this paper, a new kinematic cycle slip detection and correction method is proposed, aiming at navigation applications in urban environment with ultra high rate GPS observations. The new method has three features: first, it is based on the use of ultra high rate observations (20 Hz); second, the speed and acceleration change of the vehicle is neglected; third, code measurement is not involved. The new method is tested with practical ultra high rate GPS observations in urban environment and compared with ionospheric residual method and time relative method. The numerical results show that the new method performs obviously better than the others with all cycle slips detected and determined reliably.