The energy and time variables of the elementary classical dynami-cal systems are described geometrically, as canonically conjugate coordinates of an extended phase-space. It is shown that the Galilei action of the inertial equivalence group on this space is canonical, but not Hamiltonian equivari-ant. Although it has no effect at classical level, the lack of equivariance makes the Galilei actio...

We apply van Emde Boas-type stratified trees to point location problems in rectangular subdivisions in 2 and 3 dimensions. In a subdivision with n rectangles having integer coordinates from [1, U], we locate an integer query point in O«loglog U)d) query time using O(n) space when d ~ 2 or O(nloglogU) space when d = 3. Applications and extensions of this ''fixed universe" approach include point ...

We introduce a relativistic splitting structure as a means to map fields and equations of electromagnetism from curved four-dimensional space-time to threedimensional observer’s space. We focus on a minimal set of mathematical structures that are directly motivated by the language of the physical theory. Spacetime, world-lines, time translation, space platforms, and time synchronization all fin...

The most classic approach to the dynamics of an n-dimensional mechanical system constrained by d independent holonomic constraints is to pick explicitly a new set of (n−d) curvilinear coordinates parametrizing the manifold of configurations satisfying the constraints, and to compute the Lagrangian generating the unconstrained dynamics in these (n−d) configuration coordinates. Starting from this...

The kinematics on spatially flat FLRW space-times is presented for the first time in co-moving local charts with physical coordinates, i. e. cosmic and Painlev\' e-type Cartesian space coordinates. It shown that there exists a conserved momentum which determines form of covariant four-momentum geodesics terms Moreover, help one identifies peculiar separating recessional motions without ambiguit...