Related papers: On the Velocity Tensors
Basic notions of continuous media mechanics are introduced for spaces with affine connections and metrics. The physical interpretation of the notion of relative acceleration is discussed. The notions of deformation acceleration, shear…
A covariant hamiltonian formalism for the dynamics of compact spinning bodies in curved space-time in the test-particle limit is described. The construction allows a large class of hamiltonians accounting for specific properties and…
The purpose of the paper is to develop further a projection variational approach in relativistic hydrodynamics. The approach, previously proposed in [gr-qc/9908032], is based on the variation of the vector field and the projection tensor…
The influence of the torsion on the relative velocity and on the relative acceleration between particles (points) in spaces with an affine connection and a metric [$(L_n,g)$-spaces] and in (pseudo) Riemannian spaces with torsion…
In this paper we introduce a class of mathematical objects called \emph{extensors} and develop some aspects of their theory with considerable detail. We give special names to several particular but important cases of extensors. The…
We present a new derivation of the expressions for momentum and energy of a relativistic particle. In contrast to the procedures commonly adopted in textbooks, the one suggested here requires only the knowledge of the composition law for…
We generalize the definition of convolution of vectors and tensors on the 2-sphere, and prove that it commutes with differential operators. Moreover, vectors and tensors that are normal/tangent to the spherical surface remain so after the…
It made that the new symmetric property, the binary law, existed newly in our time and space at the thing except the symmetric property of the principle of general relativity which is already known in this paper clear. The introduction of…
In a previous paper, we proposed an approach for the dynamics of 3D bodies and shells based on the use of affine tensors. This new theoretical frame is very large and the applications are not limited to the mechanics of continua. In the…
A movable inclusion in an elastic material oscillates as a rigid body with six degrees of freedom. Displacement/rotation and force/moment tensors which express the motion of the inclusion in terms of the displacement and force at arbitrary…
In this paper we revisit the concept of chaotic velocity within the context of relativistic kinetic theory. Its importance as the key ingredient which allows to clearly distinguish convective and dissipative effects is discussed to some…
Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address…
This paper describes general relativity at the gravito-electromagnetic precision level as a constrained field theory. In this novel formulation, the gravity field comprises two auxiliary fields, a static matter field and a moving matter…
In this contribution I intend to give a summary of the new relevant results obtained by using the general superenergy tensors. After a quick review of the definition and properties of these tensors, several of their mathematical and…
We introduce a new combinatorial invariant, which we call crosscut poset, that is finer than the crosscut complex. We exhibit many applications of the crosscut poset which include a generalization of Bj\"orner's crosscut theorem and two…
The algebra of the relativistic composition of velocities is shown to be isomorphic to an algebraic loop defined on division algebras. This makes calculations in special relativity effortless and straightforward, unlike the standard…
It is shown that the most important effects of special and general theory of relativity can be understood in a simple and straightforward way. The system of units in which the speed of light $c$ is the unit of velocity allows to cast all…
This paper is a modern exposition of old ideas. The setting is a Euclidian space $E$ of dimension $n$ with associated vector space $V$ of dimension $n$. A (non-zero) sliding vector is a vector in $V$ that is free to move, but only within a…
The main concepts of the theory of tensors are presented. The emphasis is on the basic notions of tensor algebra and practical skills in culculations involving the Kronecker delta and Levi-Civita symbol. Sixty routine exercises are…
The algebra of fourvectors is described. The fourvectors are more appropriate than the Hamilton quaternions for its use in Physics and the sciences in general. The fourvectors embrace the 3D vectors in a natural form. It is shown the…