The time-optimal trajectory for an airplane from some starting point to some final point is studied by many authors. Here, we consider the extension of robot planer motion of Dubins model in three dimensional spaces. In this model, the system has independent bounded control over both the altitude velocity and the turning rate of airplane movement in a non-obstacle space. Here, in this paper a g...

the time-optimal trajectory for an airplane from some starting point to some final point is studied by many authors. here, we consider the extension of robot planer motion of dubins model in three dimensional spaces. in this model, the system has independent bounded control over both the altitude velocity and the turning rate of airplane movement in a non-obstacle space. here, in this paper a g...

in this article we review an algebraic definition of the gyrogroup and a simplified version of the gyrovector space with two fundamental examples on the open ball of finite-dimensional euclidean space, which are the einstein and möbius gyrovector spaces. we introduce the structure of gyrovector space and the gyroline on the open convex cone of positive definite matrices and see its interest...

Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. It is defined as a function on tangent bundle of a manifold. We use the Bianchi identities satisfied by Chern curvature to set up a gravitation theory in Berwald-Finsler space. The geometric part of the gravitational field equation is nonsymmetric i...

It is reasonably well-known that birefringent crystal optics can to some extent be described by the use of pseudo–Finslerian spacetimes (an extension of the natural pseudo-Riemannian Minkowski spacetime one encounters in mono-refringent situations). What is less commonly appreciated is that there are two separate and quite disjoint pseudo–Finsler structures for the two photon polarizations, and...

In the present paper we submit for study a new class of Finsler spaces. Through restricting the homogeneity condition from the definition of a complex Finsler metric to real scalars, λ ∈ R, is obtained a wider class of complex spaces, called by us the R−complex Finsler spaces. Two subclasses are taken in consideration: the Hermitian and the non-Hermitian R−complex Finsler spaces. In an R−comple...