Related papers: Kinematics of vector fields
Vector algebra is a powerful and needful tool for Physics but unfortunately, due to lack of mathematical skills, it becomes misleading for first undergraduate courses of science and engineering studies. Standard vector identities are…
A notion of Cartan pairs as an analogy of vector fields in the realm of noncommutative geometry has been proposed in q-alg/9609011 In this paper we give an outline of the construction of a noncommutative analogy of the algebra of partial…
New splitting theorems in a semi-Riemannian manifold which admits an irrotational vector field (not necessarily a gradient) with some suitable properties are obtained. According to the extras hypothesis assumed on the vector field, we can…
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of extensor fields is present using algebraic and analytical tools developed in previous papers. Several important formulas are derived.
From the principle that there is no absolute description of a physical state, we advance the approach according to which one should be able to describe the physics from the perspective of a quantum particle. The kinematics seen from this…
We use the notion of isomorphism between two invariant vector fields to shed new light on the issue of linearization of an invariant vector field near a relative equilibrium. We argue that the notion is useful in understanding the passage…
We present pictorial means of distinguishing contravariant vectors (or simply vectors) from covariant vectors (or linear forms). When one depicts vector as the directed segment, then the pictorial image of a linear form is a family of…
Vector fields with components which are generalized zero-forms are constructed. Inner products with generalized forms, Lie derivatives and Lie brackets are computed. The results are shown to generalize previously reported results for…
Vector is a physical quantity and it does not depend on any co-ordinate system. It need to be expanded in some basis for practical calculation and its components do depend on the chosen basis. The expansion in orthonormal basis is…
We introduce in the framework of the linear approximation of General relativity a natural distinction between General gauge transformations generated by any vector field and those Special ones for which this vector field is a gradient. This…
We advance an universal approach to the construction of kinematics in non-inertial and, in particular, rotating reference frames. On its basis a 10-dimensional space including three projections of velocity vector and three turn angles in…
A gravitational field can be seen as the anholonomy of the tetrad fields. This is more explicit in the teleparallel approach, in which the gravitational field-strength is the torsion of the ensuing Weitzenboeck connection. In a tetrad…
Differential calculus on the space of asymptotically linear curves is developed. The calculus is applied to the vortex filament equation in its Hamiltonian description. The recursion operator generating the infinite sequence of commuting…
Discussed is relationship between nonlinearity and symmetry of dynamical models. The special stress is laid on essential, non-perturbative nonlinearity, when none linear background does exist. This is nonlinearity essentially different from…
We present a framework for studying the dynamics of equivariant vector fields near relative equilibria. To overcome the lack of linearization at a relative equilibrium or the possible non-smoothness of the orbit space, we categorify the…
We consider theories for scalar and vector fields coupled to the energy-momentum tensor. Since these fields also carry a non-trivial energy-momentum tensor, the coupling prescription generates self-interactions. In analogy with gravity…
The mesochronic velocity is the average of the velocity field along trajectories generated by the same velocity field over a time interval of finite duration. In this paper we classify initial conditions of trajectories evolving in…
We derive slow-roll conditions for a scalar field which is non-minimally coupled with gravity in a consistent manner and express spectral indices of scalar/tensor perturbations in terms of the slow-roll parameters. The conformal invariance…
A linear connection is associated to a nonlinear connection on a vector bundle by a linearization procedure. Our definition is intrinsic in terms of vector fields on the bundle. For a connection on an affine bundle our procedure can be…
We consider a family of vector fields defined in some bounded domain of R^p, and we assume that they satisfy Hormander's rank condition of some step r, and that their coefficients have r-1 continuous derivatives. We extend to this nonsmooth…