Дисертації з теми "Injection into geodesic motion"

Gravitational waves detection is a challenging scientific objective, faced by scientist in the last 100 years, when Einstein theorized their existence. Despite multiple attempts, it was only in 2016 that the first observation of a gravitational wave was officially announced. The observation, worth a Nobel Prize, was made possible thanks to a worldwide collaboration of three large ground-based detectors. When detecting gravitational waves from ground, the noisy environment limits the frequency bandwidth of the measurement. Thus, the type of cosmic events that are observable is also limited. For this reason, scientists are developing the first gravitational waves detector based in space, which is a much quieter environment, especially in the sub-Hertz bandwidth. The space-based detector is named laser interferometer space antenna (LISA) and its launch is planned for 2034. Due to the extreme complexity of the mission, involving several new technologies, a demonstrator of LISA was launched and operated between 2015 and 2017. The demonstrator mission, called LISA Pathfinder (LPF), had the objective to show the feasibility of the gravitational waves observation directly from space, by characterizing the noise affecting the relative acceleration of two free falling bodies in the milli-Hertz bandwidth. The mission was a success, proving the expected noise level is well below the minimum requirement. The free-falling bodies of LPF, called test masses (TMs), were hosted inside dedicated electrode housings (EH), located approximately 30 cm apart inside the spacecraft. When free falling, each TM stays approximately in the center of the EH, thus having milli-meter wide gaps within the housing walls. Due to the presence of such large gaps, the TMs were mechanically constrained by dedicated mechanisms (named CVM and GPRM) in order to avoid damaging the payload during the launch phase and were released into free fall once the spacecraft was in orbit. Prior to the start of the science phase, the injection procedure of the TMs into free-fall was started. Such a procedure brought each TM from being mechanically constrained to a state where it was electro-statically controlled in the center of the EH. Surprisingly, the mechanical separation of the release mechanism from the TM caused unexpected residual velocities, which were not controllable by the electrostatic control force responsible for capturing the TM once released. Therefore, both the TMs collided with either the surrounding housing walls or the release mechanism end effectors. It was possible to start the science phase by manually controlling the release mechanism adopting non-nominal injection strategies, which should not be applicable in LISA, due to the larger time lag. So, since any release mechanism malfunctioning may preclude the initialization of LISA science phase, the GPRM was extensively tested at the end of LPF, by means of a dedicated campaign of releases, involving several modifications to the nominal injection procedure. The data of the extended campaign are analyzed in this work and the main conclusion is that no optimal automated release strategy is found for the GPRM flight model as-built configuration that works reliably for both the TMs producing a nominal injection procedure. The analysis of the in-flight data is difficult since the gravitational referencesensor of LPF is not designed for such type of analysis. In particular, the low sampling frequency (i.e., 10 Hz) constitutes a limiting factor when detecting instantaneous events such as collisions of the TM. Despite the difficulties of extracting useful information on the TM residual velocity from the in-flight data, it is found that the main cause of the uncontrollable state of the released TM is the collision of the TM with the plunger, i.e., one of the end-effectors of the GPRM. It is shown that the impact is caused by the oscillation of the plunger or by the elastic relaxation of the initial preload force that holds the TM. At the end of the analysis, some improvements to the design of the release mechanism are brie y discussed, aimed at maximizing the probability of performing a successful injection procedure for the six TMs that will be used as sensing bodies in the LISA experiment.

The work presented in this thesis is devoted to the study of geodesic motion in the context of General Relativity. The motion of a single test particle is governed by the geodesic equations of the given space-time, nevertheless one can be interested in the collective behavior of a family (congruence) of test particles, whose dynamics is controlled by the Raychaudhuri equations. In this thesis, both the aspects have been considered, with great interest in the latter issue. Geometric quantities appear in these evolution equations, therefore, it goes without saying that the features of a given space-time must necessarily arise. In this way, through the study of these quantities, one is able to analyze the given space-time. In the first part of this dissertation, we study the relation between geodesic motion and gravity. In fact, the geodesic equations are a useful tool for detecting a gravitational field. While, in the second part, after the derivation of Raychaudhuri equations, we focus on their applications to cosmology. Using these equations, as we mentioned above, one can show how geometric quantities linked to the given space-time, like expansion, shear and twist parameters govern the focusing or de-focusing of geodesic congruences. Physical requirements on matter stress-energy (i.e., positivity of energy density in any frame of reference), lead to the various energy conditions, which must hold, at least in a classical context. Therefore, under these suitable conditions, the focusing of a geodesics "bundle", in the FLRW metric, bring us to the idea of an initial (big bang) singularity in the model of a homogeneous isotropic universe. The geodesic focusing theorem derived from both, the Raychaudhuri equations and the energy conditions acts as an important tool in understanding the Hawking-Penrose singularity theorems.

Present and future space missions rely on systems of increasingly demanding performance for being successful. Drag-free technology is one of the technologies that is fundamental for LISA-Pathfinder, a European Space Agency mission whose launch is planned for the end of September 2015. A purely drag-free object is defined by the absence of all external forces other than gravity. This is not a natural condition and therefore a shield has to be used in order to eliminate the effect of undesired interactions. In space, this is achieved by properly designing the spacecraft that surrounds the object, usually called test mass (TM). Once the TM is subjected to gravity alone its motion is used as a reference for the spacecraft orbit. The satellite orbit is controlled by measuring the relative TM-to-spacecraft position and feeding back the command to the propulsion system that counteracts any non gravitational force acting on the spacecraft. Ideally, the TM should be free from all forces and the hosting spacecraft should follow a pure geodesic orbit. However, the purity of the orbit depends on the spacecraft’s capability of protecting the TM from disturbances, which indeed has limitations. According to a NASA study, such a concept is capable of decreasing operation and fuel costs, increasing navigation accuracy. At the same time, a drag-free motion is required in many missions of fundamental physics. eLISA is an ESA concept mission aimed at opening a new window to the universe, black holes, and massive binary systems by means of gravitational waves. This mission will be extremely challenging and needs to be demonstrated in flight. LISA-Pathfinder is in charge of proving this concept by demonstrating the possibility of reducing the non-gravitational disturbance below a certain demanding threshold. The success of this mission relies on recent technologies in the field of propulsion, interferometry, and space mechanisms. In this frame, the system holding the TM during launch and releasing it in free-fall before the science phase represents a single point of failure for the whole mission. This thesis describes the phenomena, operations, issues, tests, activities, and simulations linked to the release following a system engineering approach. Great emphasis is given to the adhesion (or cold welding) that interferes with the release. Experimental studies have been carried out to investigate this phenomenon in conditions representative of the LISA-Pathfinder flight environment. The last part of the thesis is dedicated to the preliminary design of the housing of the TM in the frame for a low-cost mission conceived at Stanford (USA). Analysis and results are through out presented and discussed. The goal of this thesis is a summary of the activities aimed at a successful LISA-Pathfinder mission. The ambition is to increase the maturity of the technology needed in drag-free projects and therefore provide a starting point for future fascinating and challenging missions of this kind.

Classical General Relativity predicts the existence of space-times with non-trivial casual structures known as Black Holes. A classical black hole could form by the gravitational collapse of a compact object, which should end into a singularity covered by a (sharply defined) horizon, with a size equal to the gravitational radius of the matter source. In a quantum theory, the matter source is described by a quantum state, and one can correspondingly describe its gravitational radius by means of a Horizon Wave-Function. The resulting space-time is therefore expected to be "fuzzy", and so will be the geodesic motion of test particles. Orbits of massive particles as well as trajectories of light rays around such fuzzy gravitational sources are here analysed in details using both analytical approximations and numerical calculations. The uncertainty in the time of radial free fall and the effects on the out-going radiation emitted by the collapsing matter will also be presented.

Observations of enhanced conductivity in ferroelectric domain walls have led to many new electronic applications being envisioned, such as domain wall memistors. A crucial prerequisite to realising such devices is the control over the nucleation and position of the domain walls. This thesis presents different methods of exerting this control in mesoscale ferroelectric capacitors. Investigations 'Were carried out using thin single-crystal slices of the uniaxial ferroelectric KTiOP04 (KTP), embedded into a co-planar capacitor structure. Piezoresponse Force Microscopy (PFM) showed the domain nucleation positions in these capacitors were unpredictable. As ferroelectric domains switch polarisation with an applied electric field, inhomogeneous electric field distributions were created by design in KTP lamellae using Focused Ion Beam (FIB) milled holes and patterned electrode geometries. This inhomogeneity produced localised regions of enhanced field (hot-spots) and diminished field (cold-spots). Investigations showed that when a switching field was applied to these samples, nucleation initialised at the hot-spot locations, injecting domain wall pairs. This meant that the ferroelectric could be engineered to allow site-specific injection of domain walls. These results were extended by creating different magnitudes of hot-spots, allowing the sequential injection of domain walls, to provide multiple domain states required for a domain wall memristor. Further investigation showed that hot-spots Increased domain wall mobility whereas cold-spots could pin domain walls. This effect was utilised to create asymmetric domain wall mobilities and periodic pinning sites, prerequisites for domain wall ratchet devices. Finally, investigations using variations in the ferroelectric thickness were carried out. Switching occurred in smaller thicknesses first, with positive thickness gradients yielding decreased domain wall mobility. A ferroelectric with a ramped topography, then allowed the makings of the first ferroelectric domain wall diode.

Thesis (MSc)--Stellenbosch University, 2013.
ENGLISH ABSTRACT: In this thesis I study compact objects described by the Manko-Novikov spacetime. The Manko- Novikov spacetime is an exact solution to the Einstein Field Equations that allows objects to be black hole-like, but with a multipole structure di erent from Kerr black holes. The aim of the research is to investigate whether we will observationally be able to tell these bumpy black holes, if they exist, apart from traditional Kerr black holes. I explore the geodesic motion of a test probe in the Manko-Novikov spacetime. I quantify the motion using Poincar e maps and rotation curves. The Manko-Novikov spacetime admits regions with regular motion as well as regions with chaotic motion. The occurrence of chaos is correlated with orbits for which the characteristic frequencies are resonant. The new result presented in this thesis is a global characterisation of where resonances and thus chaos are likely to occur for all orbits. These calculations are performed in the Kerr spacetime, from which I obtain that low order resonances occur within 20 Schwarzschild radii (or 40M) of the compact object with mass M. By the KAM theorem, the occurrence of chaos is therefore limited to this region for all small perturbations from Kerr. These resonant events will be measurable in the Galactic Centre using eLISA. This con nement of low order resonances indicates that the frequency values of orbits of radii well outside of 20 Schwarzschild radii can be approximated using canonical perturbation theory.
AFRIKAANSE OPSOMMING: In hierdie tesis word kompakte voorwerpe bestudeer soos omskryf deur die Manko-Novikov ruimtetyd. Die Manko-Novikov ruimtetyd is 'n eksakte oplossing van die Einstein Veldvergelykings. Die Manko-Novikov ruimtetyd formuleer gravitasiekolk-tipe voorwerpe waarvan die veelpool-struktuur afwyk van die tradisionele Kerr gravitasiekolk-struktuur. Die oogmerk van die navorsing is om vas te stel of ons met behulp van waarnemings hierdie bonkige gravitasiekolke van die tradisionele Kerr gravitasiekolke kan onderskei. Ek ondersoek die geodetiese beweging van 'n toetsmassa in die Manko-Novikov ruimtetyd. Die beweging word gekwanti seer met behulp van Poincar e afbeeldings en rotasiekrommes. In die Manko-Novikov ruimtetyd identi seer ek gebiede waarbinne re elmatige beweging voorkom asook gebiede waarbinne chaotiese bane voorkom. Die ontstaan van chaos word geassosieer met bane waarvan die fundamentele frekwensies resonant is. 'n Nuwe resultaat wat in hierdie tesis voorgehou word behels 'n globale karakterisering wat aandui waar resonansies en dus chaos na alle waarskynlikheid voorkom. Laasgenoemde berekeninge word vir die Kerr ruimtetyd uitgevoer. Hierdeur toon ek alle lae orde resonansies kom voor binne 20 Schwarzschild radii (of 40M) vanaf die kompakte voorwerp met mass M. Die KAM Stelling bepaal dan dat vir alle klein steurings toegepas op die Kerr ruimtetyd die voorkoms van chaos beperk sal wees tot bogenoemde gebied. Die resonansies binne hierdie gebied sal deur eLISA in die sentrum van die melkwegstelsel gemeet kan word. Hierdie beperking van lae orde resonansies tot 'n sekere afstand vanaf die kompakte voorwerp verseker dat die frekwensies van bane wat buite hierdie gebied val, akkuraat deur kanoniese steuringsteorie bepaal kan word.

Radiation therapy (RT) is commonly used to treat patients with lung cancer. One of the limitations of RT is that irradiation of the surrounding healthy lung tissues during RT may cause damage to the lungs. Radiation-induced pulmonary toxicity may be mitigated by minimizing doses to high-function lung tissues, which we refer to as functional avoidance RT. Lung function can be computed by image registration of treatment planning four-dimensional computed tomography (4DCT), which we refer to as CT ventilation imaging. However, the accuracy of functional avoidance RT is limited by lung function imaging accuracy and artifacts in 4DCT. The goal of this dissertation is to improve the accuracy of functional avoidance RT by overcoming those two limitations. A common method for estimating lung ventilation uses image registration to align the peak exhale and inhale 3DCT images. This approach called the 2-phase local expansion ratio is limited because it assumes no out-of-phase lung ventilation and may underestimate local lung ventilation. Out-of-phase ventilation occurs when regions of the lung reach their maximum (minimum) local volume in a phase other than the peak of inhalation (end of exhalation). This dissertation presents a new method called the N-phase local expansion ratio for detecting and characterizing locations of the lung that experience out-of-phase ventilation. The N-phase LER measure uses all 4DCT phases instead of two peak phases to estimate lung ventilation. Results show that out-of-phase breathing was common in the lungs and that the spatial distribution of out-of-phase ventilation varied from subject to subject. On average, 49% of the out-of-phase regions were mislabeled as low-function by the 2-phase LER. 4DCT and Xenon-enhanced CT (Xe-CT) of four sheep were used to evaluate the accuracy of 2-phase LER and N-phase LER. Results show that the N-phase LER measure was more correlated with the Xe-CT than the 2-phase LER measure. These results suggest that it may be better to use all 4DCT phases instead of the two peak phases to estimate lung function. The accuracy of functional avoidance RT may also be improved by reducing the impact of artifacts in 4DCT. In this dissertation, we propose a a geodesic density regression (GDR) algorithm to correct artifacts in one breathing phase by using artifact-free data in corresponding regions of the other breathing phases. Local tissue density change associated with CT intensity change during respiration is accommodated in the GDR algorithm. Binary artifact masks are used to exclude regions of artifacts from the regression, i.e., the GDR algorithm only uses artifact-free data. The GDR algorithm estimates an artifact-free CT template image and its time flow through a respiratory cycle. Evaluation of the GDR algorithm was performed using both 2D CT time-series images with simulated known motion artifacts and treatment planning 4DCT with real motion artifacts. The 2D results show that there is no significant difference (p-value = 0.95) between GDR regression of artifact data using artifact masks and regression of artifact-free data. In contrast, significant errors (p-value = 0.005) were present in the estimated Jacobian images when artifact masks were not used. We also demonstrated the effectiveness of the GDR algorithm for removing real duplication, misalignment, and interpolation artifacts in 4DCT. Overall this dissertation proposes methods that have the potential to improve functional avoidance RT by accommodating out-of-phase ventilation, and removing motion artifacts in 4DCT using geodesic image regression.

Objective - To investigate the effects of injected protease solution on the mechanical advancement of disc degeneration, and to establish test protocol for future pre-clinical validation of spinal arthroplasty devices. The hypothesis that injection of a protease into a cadaveric lumbar disc will mimic advanced degeneration mechanics was the subject of this study. Summary of Background Information - Spinal disc degeneration is a universal condition that progresses in adults due to aging, disease, or injury. Stages of disc degeneration have been categorized in cadaver specimens, with each degeneration level exhibiting characteristic changes in flexibility parameters. Spinal disc tissue can be compromised through introduction of proteolytic enzymes into the collagenous fibers of the annulus fibrosus. Methods - 18 motion segments from 8 human lumbar spines were subjected to flexibility testing. Each specimen was either injected with 0.600 mL of trypsin solution in the annulus fibrosus, 0.600 mL of phosphate-buffed saline, or a fluid-less needle-stick. Motion testing followed with rotations applied in all three major spinal motions. Test sections were transected mid-disc after testing to characterize initial degeneration severity, and acquired motion data was analyzed to show flexibility traits over time. Results - Trypsin, saline, and control injections all caused changes in motion from pre-injection baselines. Saline injections were slightly more effective at mimicking the mechanics of higher grades of degeneration with more fidelity than trypsin injections. All motion parameters were altered by the study treatments, with hysteresis and neutral zone parameters experiencing changes similar to that seen in natural degeneration with greater fidelity. Lateral Bending motion showed the greatest magnitude response to injections, with Flexion-Extension tests showing the smallest change. Discussion - Unexpectedly, fluid-less control injections caused changes to hysteresis and neutral zone parameters, suggesting an alteration to viscoelastic properties due to simple needle puncture. Fluid injections (Trypsin and Saline) caused an immediate transient post-injection change to biomechanics that dissipated over time, except in Axial Rotation. Saline injections provided the highest fidelity in mimicking the motion of more advanced stages of degeneration.

The objective of the dissertation is to develop simplified analytical models for typical linear-motion and rotary-motion energy-conversion systems under active DC excitation without tedious numerical-simulation effort, and provide practical implementation of the models in optimal-design and thermal-protection aspects. The model of a vacuum automatic circuit recloser (a typical linear-motion system under DC excitation) is first developed in the form of a non-linear discontinuous eighth-order dynamic system. The model is then used to simulate the transient mechanical and electromagnetic performance during the opening and closing movements of the recloser. Such a model is not found in the literature. Although the model is based on certain simplifying assumptions, the result is validated by high-speed-camera measurements. In addition, the impact of key design variables is explored, based on which an improved recloser design is proposed, and helps to optimize capital and production costs without degrading performance. Further analytical investigation is carried out in modeling an inverter-fed induction motor (IM) (a typical rotary-motion system) with active DC injection. The IM is closed-loop controlled via two popular motor-control algorithms, namely, the direct-torque-control (DTC) algorithm and field-oriented-control (FOC) algorithm. Quantitative relationships between the changes of various machine variables during the active DC excitation are provided in the theoretical analysis. The developed DC-injection model is further simplified for practical implementation. The developed IM model under DC injection results in practical ways to excite a proper amount of DC current directly or indirectly into IM stator windings via different closed-loop motor-control algorithms. In a DTC motor-drive system, the modeling work makes it possible to excite the DC current indirectly inside the motor by superimposing a stator-flux-linkage-bias command in the flux-control loop or a torque-ripple command in the torque-control loop. The proposed flux-linkage-injection and torque-injection methods are the first novel efforts to implement the DC-signal-injection method in a DTC motor-drive system. In addition, the analysis carried out in a standard FOC drive system brings about an improved DC-current-injection approach: the torque ripple in this method is significantly mitigated compared to all existing DC-injection methods in FOC systems. The proposed DC-injection methods, either in a DTC or an FOC system, lead to a simple, low-cost, accurate, and non-invasive thermal-monitoring scheme for closed-loop-controlled IMs, where the stator temperature is indirectly estimated from stator resistance. Furthermore, considering inverter non-idealities, there is a challenge for a typical inverter drive to accurately estimate the DC component of motor terminal voltages. The existing methods are extended to provide a complete study of the real-time signal-processing technique for both DTC and FOC algorithms, and are finally implemented in a custom-built programmable motor-drive system. The experimental results demonstrate that the proposed technique gives accurate and robust stator-temperature estimation, regardless of the operating conditions and cooling modes. The analytical modeling method for the linear-motion and rotary-motion energy-conversion systems can be further extended to other power devices with similar mechanisms, and implemented in optimal design, control, and thermal-protection areas.

Cette étude introduit une nouvelle approche appelée Bivariate 2D-EMD pour séparer le mouvement organisé à grande échelle, soit la composante basse fréquence de l’écoulement des fluctuations turbulentes, soit la composante haute fréquence dans un champ de vitesse instantané bidimensionnel.Cette séparation nécessite un seul champ de vitesse instantané contrairement aux autres méthodes plus couramment utilisées en mécanique des fluides, comme le POD. La méthode proposée durant cette thèse est tout à fait appropriée à l’analyse des écoulements qui sont intrinsèquement instationnaires et non linéaires comme l'écoulement dans le cylindre lorsque le moteur fonctionne dans des conditions transitoires. Bivariate 2D-EMD est validé à travers différents cas test, sur un écoulement turbulent homogène et isotrope (THI) expérimental, qui a été perturbé par un tourbillon synthétique de type Lamb-Ossen, qui simule le mouvement organisé dans le cylindre. Enfin, Il est appliqué sur un écoulement expérimental obtenu dans un cylindre et les résultats de la séparation d'écoulement sont comparés à ceux basés sur l'analyse POD. L’évolution d’écoulement dans le cylindre pendant le fonctionnement du moteur transitoire, c’est à dire une accélération du régime moteur de 1000 à 2000tr/min en différentes rampes, sont mesurée en utilisant de PIV 2D-2C haute cadence. Les champs de vitesse sont obtenus dans le plan de tumble dans un moteur un moteur GDI mono-cylindre transparent et forment une base de données nécessaire pour valider les résultats de simulation numérique
This study introduces a new approach called Bivariate 2D-EMD to separate large-scale organizedmotion i.e., flow low frequency component from random turbulent fluctuations i.e., high frequency onein a given in-cylinder instantaneous 2D velocity field. This signal processing method needs only oneinstantaneous velocity field contrary to the other methods commonly used in fluid mechanics, as POD.The proposed method is quite appropriate to analyze the flows intrinsically both unsteady and nonlinearflows as in in-cylinder. The Bivariate 2D-EMD is validated through different test cases, by optimize itand apply it on an experimental homogeneous and isotropic turbulent flow (HIT), perturbed by asynthetic Lamb-Ossen vortex, to simulate the feature of in-cylinder flows. Furthermore, it applies onexperimental in-cylinder flows. The results obtained by EMD and POD analysis are compared. Theevolution of in-cylinder flow during transient engine working mode, i.e., engine speed acceleration from1000 to 2000 rpm with different time periods, was obtained by High speed PIV 2D-2C. The velocityfields are obtained within tumble plane in a transparent mono-cylinder DISI engine and provide a database to validate CFD

As a non-linear theory of space-time, general relativity deals with interesting dynamical systems which can be expected more prone to chaos than their Newtonian counter-parts. In this thesis, we study the dynamics of time- like geodesics in the static and axisymmetric field of a Schwarzschild black hole surrounded, in a concentric way, by a massive thin disc or ring. We reveal the rise (and/or decline) of geodesic chaos in dependence on parameters of the sys- tem (the disc/ring mass and position and the test-particle energy and angular momentum), (i) on Poincaré sections, (ii) on time series of position and their power spectra, (iii) by applying two simple yet powerful recurrence methods, and (iv) by computing Lyapunov exponents and two other related quantifiers of or- bital divergence. We mainly focus on "sticky" orbits whose different parts show different degrees of chaoticity and which offer the best possibility to test and compare different methods. We also add a treatment of classical but dissipative system, namely the evolution of a class of mechanical oscillators described by non-standard constitutive relations.

We study the dynamics of time-like geodesics in the field of black holes perturbed by a circular ring or disc, restricting to static and axisymmetric class of space-times. Two analytical methods are tested which do not require solving the equations of motion: (i) the so-called geometric criterion of chaos based on eigenvalues of the Riemann tensor, and (ii) the method of Melnikov which detects the chaotic layer arising by break-up of a homoclinic orbit. Predictions of both methods are compared with numerical results in order to learn how accurate and reliable they are.

The present dissertation develops an invariant framework for 3D gesture comparison studies. 3D gesture comparison without Lagrangian models is challenging not only because of the lack of prediction provided by physics, but also because of a dual geometry representation, spatial dimensionality and non-linearity associated to 3D-kinematics. In 3D spaces, it is difficult to compare curves without an alignment operator since it is likely that discrete curves are not synchronized and do not share a common point in space. One has to assume that each and every single trajectory in the space is unique. The common answer is to assert the similitude between two or more trajectories as estimating an average distance error from the aligned curves, provided that the alignment operator is found. In order to avoid the alignment problem, the method uses differential geometry for position and orientation curves. Differential geometry not only reduces the spatial dimensionality but also achieves view invariance. However, the nonlinear signatures may be unbounded or singular. Yet, it is shown that pattern recognition between intrinsic signatures using correlations is robust for position and orientation alike. A new mapping for orientation sequences is introduced in order to treat quaternion and Euclidean intrinsic signatures alike. The new mapping projects a 4D-hyper-sphere for orientations onto a 3D-Euclidean volume. The projection uses the quaternion invariant distance to map rotation sequences into 3D-Euclidean curves. However, quaternion spaces are sectional discrete spaces. The significance is that continuous rotation functions can be only approximated for small angles. Rotation sequences with large angle variations can only be interpolated in discrete sections. The current dissertation introduces two multi-scale approaches that improve numerical stability and bound the signal energy content of the intrinsic signatures. The first is a multilevel least squares curve fitting method similar to Haar wavelet. The second is a geodesic distance anisotropic kernel filter. The methodology testing is carried out on 3D-gestures for obstetrics training. The study quantitatively assess the process of skill acquisition and transfer of manipulating obstetric forceps gestures. The results show that the multi-scale correlations with intrinsic signatures track and evaluate gesture differences between experts and trainees.