34,277 research outputs found
The origin of the spacetime metric: Bell's `Lorentzian pedagogy' and its significance in general relativity
The purpose of this paper is to evaluate the `Lorentzian pedagogy' defended
by J.S. Bell in his essay ``How to teach special relativity'', and to explore
its consistency with Einstein's thinking from 1905 to 1952. Some remarks are
also made in this context on Weyl's philosophy of relativity and his 1918 gauge
theory. Finally, it is argued that the Lorentzian pedagogy - which stresses the
important connection between kinematics and dynamics - clarifies the role of
rods and clocks in general relativity.Comment: To be published in ``Physics Meets Philosophy at the Planck Length'',
C. Callender and N. Huggett (eds.), Cambridge University Press (1999). 22
pages, no figures, LaTeX, uses harvard.sty; 3 references added, typos
corrected and minor changes to conten
On Centroidal Dynamics and Integrability of Average Angular Velocity
In the literature on robotics and multibody dynamics, the concept of average
angular velocity has received considerable attention in recent years. We
address the question of whether the average angular velocity defines an
orientation framethat depends only on the current robot configuration and
provide a simple algebraic condition to check whether this holds. In the
language of geometric mechanics, this condition corresponds to requiring the
flatness of the mechanical connection associated to the robotic system. Here,
however, we provide both a reinterpretation and a proof of this result
accessible to readers with a background in rigid body kinematics and multibody
dynamics but not necessarily acquainted with differential geometry, still
providing precise links to the geometric mechanics literature. This should help
spreading the algebraic condition beyond the scope of geometric
mechanics,contributing to a proper utilization and understanding of the concept
of average angular velocity.Comment: 8 pages, accepted for IEEE Robotics and Automation Letters (RA-L
Robust Non-Rigid Registration with Reweighted Position and Transformation Sparsity
Non-rigid registration is challenging because it is ill-posed with high
degrees of freedom and is thus sensitive to noise and outliers. We propose a
robust non-rigid registration method using reweighted sparsities on position
and transformation to estimate the deformations between 3-D shapes. We
formulate the energy function with position and transformation sparsity on both
the data term and the smoothness term, and define the smoothness constraint
using local rigidity. The double sparsity based non-rigid registration model is
enhanced with a reweighting scheme, and solved by transferring the model into
four alternately-optimized subproblems which have exact solutions and
guaranteed convergence. Experimental results on both public datasets and real
scanned datasets show that our method outperforms the state-of-the-art methods
and is more robust to noise and outliers than conventional non-rigid
registration methods.Comment: IEEE Transactions on Visualization and Computer Graphic
Covariant Balance Laws in Continua with Microstructure
The purpose of this paper is to extend the Green-Naghdi-Rivlin balance of
energy method to continua with microstructure. The key idea is to replace the
group of Galilean transformations with the group of diffeomorphisms of the
ambient space. A key advantage is that one obtains in a natural way all the
needed balance laws on both the macro and micro levels along with two
Doyle-Erickson formulas
Subspace procrustes analysis
Postprint (author's final draft
Cross-calibration of Time-of-flight and Colour Cameras
Time-of-flight cameras provide depth information, which is complementary to
the photometric appearance of the scene in ordinary images. It is desirable to
merge the depth and colour information, in order to obtain a coherent scene
representation. However, the individual cameras will have different viewpoints,
resolutions and fields of view, which means that they must be mutually
calibrated. This paper presents a geometric framework for this multi-view and
multi-modal calibration problem. It is shown that three-dimensional projective
transformations can be used to align depth and parallax-based representations
of the scene, with or without Euclidean reconstruction. A new evaluation
procedure is also developed; this allows the reprojection error to be
decomposed into calibration and sensor-dependent components. The complete
approach is demonstrated on a network of three time-of-flight and six colour
cameras. The applications of such a system, to a range of automatic
scene-interpretation problems, are discussed.Comment: 18 pages, 12 figures, 3 table
Symmetry-Adapted Phonon Analysis of Nanotubes
The characteristics of phonons, i.e. linearized normal modes of vibration,
provide important insights into many aspects of crystals, e.g. stability and
thermodynamics. In this paper, we use the Objective Structures framework to
make concrete analogies between crystalline phonons and normal modes of
vibration in non-crystalline but highly symmetric nanostructures. Our strategy
is to use an intermediate linear transformation from real-space to an
intermediate space in which the Hessian matrix of second derivatives is
block-circulant. The block-circulant nature of the Hessian enables us to then
follow the procedure to obtain phonons in crystals: namely, we use the Discrete
Fourier Transform from this intermediate space to obtain a block-diagonal
matrix that is readily diagonalizable. We formulate this for general Objective
Structures and then apply it to study carbon nanotubes of various chiralities
that are subjected to axial elongation and torsional deformation. We compare
the phonon spectra computed in the Objective Framework with spectra computed
for armchair and zigzag nanotubes. We also demonstrate the approach by
computing the Density of States. In addition to the computational efficiency
afforded by Objective Structures in providing the transformations to
almost-diagonalize the Hessian, the framework provides an important conceptual
simplification to interpret the phonon curves.Comment: To appear in J. Mech. Phys. Solid
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