The direct geodesic problem on an oblate spheroid is described as an initial value problem and is solved numerically in geodetic and Cartesian coordinates. The geodesic equations are formulated by means of the theory of differential geometry. The initial value problem under consideration is reduced to a system of first-order ordinary differential equations, which is solved using a numerical met...

Wederive computational formulas for determining the Clairaut constant, i.e. the cosine of themaximum latitude of the geodesic arc, from two given points on the oblate ellipsoid of revolution. In all cases the Clairaut constant is unique. The inverse geodetic problem on the ellipsoid is to determine the geodesic arc between and the azimuths of the arc at the given points. We present the solution...

Abstract: The geodesic problem in Wasserstein spaces with a metric perturbed by a conformal factor is considered, and necessary optimality conditions are estabilished in a case where this conformal factor favours the spreading of the probability measure along the curve. These conditions have the form of a system of PDEs of the kind of the compressible Euler equations. Moreover, self-similar sol...

We consider the geodesic motion on the symmetric moduli spaces that arise after timelike and spacelike reductions of supergravity theories. The geodesics correpond to timelike respectively spacelike p-brane solutions when they are lifted over a pdimensional flat space. In particular, we consider the problem of constructing the minimal generating solution: A geodesic with the minimal number of f...

Many problems in Calculus of Variations require the use functionals containing several independent and dependent variables. The first part of this report covers the derivation of the Euler-Lagrange equation for the general functional involving multi-variables vectorvalued functions with fixed boundary. Some of its corollaries and applications will be explored. In the second part we focus on an ...

In this article, we study the geodesic problem in a generalized metric space, in which the distance function satisfies a relaxed triangle inequality d(x, y) ≤ σ(d(x, z) +d(z, y)) for some constant σ ≥ 1, rather than the usual triangle inequality. Such a space is called a quasimetric space. We show that many well-known results in metric spaces (e.g. Ascoli-Arzelà theorem) still hold in quasimetr...