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Riemannian metrics on 2D-manifolds related to the Euler-Poinsot rigid body motion

Riemannian metrics on 2D-manifolds related to the Euler-Poinsot rigid body motion

Abstract. The Euler−Poinsot rigid body motion is a standard mechanical system and it is a model for left-invariant Riemannian metrics on SO(3). In this article using the Serret−Andoyer variables we parameterize the solutions and compute the Jacobi fields in relation with the conjugate locus evaluation. Moreover, the metric can be restricted to a 2D-surface, and the conjugate points of this metric are evaluated using recent works on surfaces of revolution. Another related 2D-metric on S 2

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The Serret-Andoyer Riemannian metric and Euler-Poinsot rigid body motion

The Serret-Andoyer Riemannian metric and Euler-Poinsot rigid body motion

Open Archive TOULOUSE Archive Ouverte (OATAO) OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web[r]

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A boundary control problem for the steady self-propelled motion of a rigid body in a Navier-Stokes fluid

A boundary control problem for the steady self-propelled motion of a rigid body in a Navier-Stokes fluid

∂Ω x × (V + v ∗ )(V · n)dγ. (3.9) Indeed the formulation (3.5) and (3.6) might look artificial, but it depends on how to develop the linear theory in the next section (there are actually some other possible ways). In order to define the control space for our problem, we consider six auxiliary adjoint problems, associated with six elementary rigid body motion velocities. For each i ∈ {1, 2, 3}, let (v (i) , q (i) ) be the solution of the generalized Oseen problem

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Riemannian metrics on 2D manifolds related to the Euler-Poinsot rigid body problem

Riemannian metrics on 2D manifolds related to the Euler-Poinsot rigid body problem

IV. C ONCLUSION We presented here two 2D models, intrinsically related to the Euler-Poinsot rigid body motion. The new theoretical result of this paper is the explicit construction of the basis of Jacobi vector fields for Darboux-type metrics on 2D surfaces of revolution. The consequences of this computation go beyond the content of this paper. From one hand, it gives an alternative and simplified proof of the conjugate locus equation that we used to describe the structure of the conjugate locus of the Serret-Andoyer metric. On the other hand, even if this result gives no information on the conjugate
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Rapid determination of RMSDs corresponding to macromolecular rigid body motions

Rapid determination of RMSDs corresponding to macromolecular rigid body motions

2 Laboratoire Jean Kuntzmann, B.P. 53, 38041 Grenoble Cedex 9, France February 26, 2014 Abstract Finding the root mean sum of squared deviations (RMSDs) between two coordinate vec- tors that correspond to the rigid body motion of a macromolecule is an important problem in structural bioinformatics, computational chemistry and molecular modeling. Standard algo- rithms compute the RMSD with time proportional to the number of atoms in the molecule. Here, we present RigidRMSD, a new algorithm that determines a set of RMSDs correspond- ing to a set of rigid body motions of a macromolecule in constant time with respect to the number of atoms in the molecule. Our algorithm is particularly useful for rigid body modeling applications such as rigid body docking, and also for high-throughput analysis of rigid body modeling and simulation results. We also introduce a constant-time rotation RMSD as a sim- ilarity measure for rigid molecules. A C++ implementation of our algorithm is available at http://nano-d.inrialpes.fr/software/RigidRMSD.
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Coupling rigid bodies motion with single phase and two-phase compressible flows on unstructured meshes

Coupling rigid bodies motion with single phase and two-phase compressible flows on unstructured meshes

University of Nice, LJAD UMR CNRS 7351, Parc Valrose, 06108 Nice Cedex, France Abstract A simple method is developed to couple accurately the motion of rigid bodies to compressible fluid flows. Solid rigid bodies are tracked through a Level-Set function. Numerical diffusion is controlled thanks to a compressive limiter (Overbee) in the frame of MUSCL type scheme, giving an excellent compromise between accuracy and efficiency on unstructured meshes (Chiapolino et al., 2017). The method requires low resolution to preserve solid bodies’ volume. Several coupling methods are then addressed to couple rigid body motion to fluid flow dynamics: a method based on stiff relaxation and two methods based on Ghost cells (Fedkiw et al., 1999) and immersed boundaries. Their accuracy and convergence rates are compared against an immersed piston problem in 1D having exact solution. The second Ghost cell method is shown to be the most efficient. It is then extended to multidimensional computations on unstructured meshes and its accuracy is checked against flow computations around blunt bodies. Reference results are obtained when the flow evolves around a rigid body at rest. The same rigid body is then considered with prescribed velocity moving in a flow at rest. Computed results involving wave dynamics match very well. The method is then extended to two-way coupling and illustrated to several examples involving shock wave interaction with solid particles as well as phase transition induced by projectiles motion in liquid-gas mixtures.
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Estimation of Human Body Shape in Motion with Wide Clothing

Estimation of Human Body Shape in Motion with Wide Clothing

6 Evaluation 6.1 Dataset This section introduces the new dataset we acquired to allow quantitative evalu- ation of human body shape estimation from dynamic data. The dataset consists of synchronized acquisitions of dense unstructured geometric motion data and sparse motion capture (MoCap) data of 6 subjects (3 female and 3 male) cap- tured in 3 different motions and 3 clothing styles each. The geometric motion data are sequences of meshes obtained by applying a visual hull reconstruction to a 68-color-camera (4M pixels) system at 30FPS. The basic motions that were captured are walk, rotating the body, and pulling the knees up. The captured clothing styles are very tight, layered (long-sleeved layered clothing on upper body), and wide (wide pants for men and dress for women). The body shapes of 6 subjects vary significantly. Fig. 4 shows some frames of the database.
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Indoor On-body Channel Ray Tracing and Motion Capture Based Simulation

Indoor On-body Channel Ray Tracing and Motion Capture Based Simulation

The antenna pattern is expanded in terms of spherical harmonics coefficients [ 7 ],[ 8 ]. This approach reduces the amount of data required for describing the full antenna pattern. This has been the chosen manner for describing the antenna pattern in the PyLayers simulation platform. The ray tracing is used to take into account the interaction on walls of the environment. This is much more questionable to apply the ray tracing for the On-body channel. There is current

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Intensity-based visual servoing for non-rigid motion compensation of soft tissue structures due to physiological motion using 4D ultrasound

Intensity-based visual servoing for non-rigid motion compensation of soft tissue structures due to physiological motion using 4D ultrasound

Fig. 7. Rigid motion compensation results of a deformable region using simulated 4D US At first, we perform a rigid motion tracking task with an abdominal phantom. The secondary robot repeatedly rotated the abdominal phantom on a turning table in one direction and the opposite direction. In the meantime, the 6-DOF robot holding the 4D US probe is controlled by our method to automatically compensate the rigid motion of the target region within the phantom. The observed feature error and probe trajectory are shown in Fig. 9 and Fig. 10 (left). To maintain the firm contact between the probe and the phantom, we used a force control along the X axis of the 3D US image.
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Time-dependent lift and drag on a rigid body in a viscous steady linear flow

Time-dependent lift and drag on a rigid body in a viscous steady linear flow

The chief technical difficulty i n t his c lass o f p roblems i s t hat, o wing t o t he presence of a space-dependent term (the one that was overlooked by Bedeaux & Rubi ( 1987 ) and Pérez-Madrid et al. ( 1990 )), the unsteady disturbance in Fourier space is governed by a set of coupled partial differential equations. This makes it particularly difficult to obtain the solution. For the solid-body rotation, this difficulty i s e asily overcome by using a rotating reference frame, since the space-dependent term disappears in this frame (Herron et al. 1975 ; Miyazaki 1995 ; Candelier 2008 ). Based on this observation, it seems natural to seek a generic coordinate transformation that removes this term whatever the carrying flow. T his i s t he b ackbone o f t he p resent w ork. M ore precisely, we express the unsteady disturbance problem in a system of moving non-orthogonal coordinates that follow the undisturbed flow. I n F ourier s pace, t he d isturbance i s then determined by a set of ordinary differential equations in these co-moving coordinates, making the problem much easier to solve. Solving these equations and transforming back to the laboratory frame yields the desired inertial corrections irrespective of the nature of the linear carrying flow. T his t echnique i s s imilar i n e ssence t o t he approach used in the rapid distortion theory (RDT), pioneered by Batchelor & Proudman ( 1954 ) to determine how a turbulent velocity fluctuation i s d istorted b y a s trong non-uniform mean flow. I n t he p articular c ontext o f t he fl ow pa st a ri gid bo dy, th is id ea was also used by Miyazaki et al. ( 1995 ), extending a technique developed by Onuki & Kawasaki ( 1980 ) for a scalar field, b ut, c ompared t o o ur a pproach, t hey employed it differently, namely by considering time-dependent wavenumbers in the Fourier transform of the disturbance equation. These connections are discussed in more detail at the end of § 3.1 .
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Virtual fracture reduction of the acetabulum using a rigid body biomechanical model

Virtual fracture reduction of the acetabulum using a rigid body biomechanical model

in 3D space, with few or no anatomical consideration, resulting to movements that may not be realized in real surgery. A new paradigm is then to simulate the procedure itself, instead of the desired result. During surgery, bone fragments are repositioned using clamps, hooks or Schanz screws (figure 2). The fracture is then reduced via the application of forces by the physician. Moreover, the surgeon use the contacts between structures, e.g. lean the ischium on the femoral head, to produce the expected movements. To simulate such a procedure we have chosen to use a mechanical model of the hip joint bony elements, implemented within the non-commercial Artisynth framework [10]. Each bone fragment is considered as an independent rigid body. One of them is usually considered as fixed, e.g. the anterior or posterior column and/or the femoral head. Collisions are handled to ensure non-penetration between elements, with dry friction (Coulomb) response. The action of a clamp is simulated via a Hill muscle model which extremities are the clamp jaws positions on the bones. The interactive “contraction” of this model apply forces similarly to the real clamp action. In reality, the muscular system apply heavy constraints to the bones during their repositioning. While modeling this accurately is an extremely complex problem, moreover in a patient-specific context, a first approximation is to add a strong global damping to the all system. Even if preferred anatomical directions are not accounted for, this high resistance ensure the response to collisions and numerical instabilities are very low in comparison to the forces directly applied to the bones. When all these elements are set, the dynamic numerical system is solved using traditional methods (Euler implicit, Runge-Kutta…).
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Low regularity solutions for the two-dimensional ''rigid body + incompressible Euler" system.

Low regularity solutions for the two-dimensional ''rigid body + incompressible Euler" system.

[7] Marchioro C., Pulvirenti M., Mathematical theory of incompressible nonviscous fluids. Applied Mathematical Sciences 96, Springer-Verlag, 1994. [8] Ortega J., Rosier L., Takahashi T., On the motion of a rigid body immersed in a bidimensional incompressible perfect fluid, Ann. Inst. H. Poincar´e Anal. Non Lin´eaire, 24 (2007), no. 1, 139–165.

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A Batch Algorithm For Implicit Non-Rigid Shape and Motion Recovery

A Batch Algorithm For Implicit Non-Rigid Shape and Motion Recovery

We introduce theoretical and practical contributions that address these issues. We propose an implicit imaging model for non-rigid scenes from which we derive non-rigid matching tensors and closure constraints. We give a non- rigid Structure-From-Motion algorithm based on comput- ing matching tensors over subsequences, from which the im- plicit cameras are extrated. Each non-rigid matching tensor is computed, along with the rank of the subsequence, using a robust estimator incorporating a model selection criterion that detects erroneous image points.

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2D-3D rigid-body registration of X-ray flourscopy and CT images

2D-3D rigid-body registration of X-ray flourscopy and CT images

The controlled experiments used images of a phantom spine, of a real and a plastic skull, of a real head and of a lumbar plastic spine segment, and the experiments using [r]

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Local null controllability of a rigid body moving into a Boussinesq flow

Local null controllability of a rigid body moving into a Boussinesq flow

There are few articles in the last decade concerning the controllability results on fluid- structure interaction problem. In a paper of Raymond and Vanninathan [ 37 ], they considered a simplified model in 2D where the fluid equations are replaced by the Helmholtz equations and the motion of a solid represented by a harmonic oscillator. In that case, the domain is supposed to be fixed but one of the difficulties comes from the fact that there is no control in the solid part. They established exact controllability results for this model with an internal control only in the fluid part. In the work of Doubova and Fern´ andez-Cara [ 12 ], they proved the local null controllability by boundary controls for a 1D model where point mass is immersed in a fluid which evolves in p´1, 1q. In that case, the domain is not fixed any more and the proof of the result is based on the global null controllability of the linearized system (by Carleman estimates) and on Kakutani’s fixed point theorem. In [ 29 ], the authors established exact con- trollability of a 2D fluid-structure system where the body is a ball. In the paper of Boulakia and Osses [ 4 ], the authors dealt with the same problem as in [ 29 ], except that the body can have more general shape. In [ 3 ], Boulakia and Guerrero proved the local null controllability of a fluid-solid interaction problem in three dimension. Finally, in [ 34 ], the authors studied the local null controllability problem for the simplified one dimensional model considered in [ 12 ] and they managed to reduce the number of controls.
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Time-dependent lift and drag on a rigid body in a viscous steady linear flow

Time-dependent lift and drag on a rigid body in a viscous steady linear flow

Coming back to unbounded linear flows, another series of studies employed the so-called ‘induced-force’ method (hereinafter abbreviated as IF) as an alternative to the MAE approach, based on the formulation developed by Mazur & Bedeaux ( 1974 ) to extend Faxén’s formulae to a sphere undergoing an arbitrary time-dependent motion in an inhomogeneous flow. In this method, an extra force is added to the Navier–Stokes equation to ensure that the slip velocity vanishes everywhere within the body, rendering the modified equation valid in the entire domain, both in the fluid and the body. This approach was first applied by Bedeaux & Rubi ( 1987 ) to find the frequency-dependent inertial corrections to the force experienced by a sphere translating in a planar or an axisymmetric purely elongational flow. Pérez-Madrid, Rubi & Bedeaux ( 1990 ) then obtained the quasi-steady form of the friction tensor for the three canonical planar flow configurations discussed above. While their result agreed with that of Herron et al. ( 1975 ) in a solid-body rotation flow, the components of the resistance tensor obtained in the case of a pure shear flow differed from those determined by Harper & Chang ( 1968 ). In particular the component corresponding to the Saffman’s lift force was found to be approximately 2.3 times larger than predicted by the MAE approach (Harper & Chang 1968 ; Saffman 1968 ). This issue was reconsidered by Miyazaki, Bedeaux & Avalos ( 1995 ), who identified that a non-algebraic term was unduly neglected by Bedeaux & Rubi ( 1987 ) and Pérez-Madrid et al. ( 1990 ), leading to erroneous results in the quasi-steady limit (except in the solid-body rotation case where this term does not contribute to the final result). Having dealt with this term through a transformation described later, Miyazaki
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Tasks prioritization for whole-body realtime imitation of human motion by humanoid robots

Tasks prioritization for whole-body realtime imitation of human motion by humanoid robots

considered first. As a consequence, the trajectory tracking and the balance man- agement tasks dealt with already admissible trajectories. The imitation showed good results in terms of all four tasks. Fig. 2 shows the hands and foot simulta- neous trajectories of scaled human (blue) and humanoid (red) movements during on-line tracking. The distances are in [mm] for the left hand (top), the right hand (middle) and the left foot (bottom). The Cartesian values were synchronized in time, which means that the robot motion was performed 1) at the same velocity as the human motion and 2) the human movement coordination was respected. All the optimized tasks are in the kernel of the last Jacobian, which means they have equivalent priority in the proposed model. The only way to modify the or- der of priority is the tuning of the gains κ ℓ and κ h . Let us also point out that the
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Rigid and strongly rigid relations on small domains

Rigid and strongly rigid relations on small domains

We proposed several simple lemmas to exclude non-rigid binary relations which can be turned into computer programs. These lemmas are quite effective not only in a 4- element domain but also in a k-element domain when k ≥ 5. Some techniques used in recent developments in Barto and Stanovský [37] and Jovanovi´c [40] can also help in this aspect. Applying these rules to a 5-element domain, we could obtain a result as in Table 7.1. It would be interesting to find out all strongly rigid binary relations out of the potential list on a 5-element domain.

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Using Singularities of Parallel Manipulators for Enhancing the Rigid-body Replacement Design Method of Compliant Mechanisms

Using Singularities of Parallel Manipulators for Enhancing the Rigid-body Replacement Design Method of Compliant Mechanisms

jacques.gangloff@unistra.fr pierre.renaud@insa-strasbourg.fr The rigid-body replacement method is often used when de- signing a compliant mechanism. The stiffness of the com- pliant mechanism, one of its main properties, is then highly dependent on the initial choice of a rigid-body architecture. In this paper, we propose to enhance the efficiency of the syn- thesis method by focusing on the architecture selection. This selection is done by considering the required mobilities and parallel manipulators in singularity to achieve them. Kine- matic singularities of parallel structures are indeed advan- tageously used to propose compliant mechanisms with inter- esting stiffness properties. The approach is first illustrated by an example, the design of a one degree of freedom compliant architecture. Then the method is used to design a medical device where a compliant mechanism with three degrees of freedom is needed. The interest of the approach is outlined after application of the method.
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Computing Structure and Motion of General 3D Rigid Curves from Monocular Sequences of Perspective Images

Computing Structure and Motion of General 3D Rigid Curves from Monocular Sequences of Perspective Images

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignemen[r]

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