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Summary

This chapter discusses some basic spherical trigonometry applicable to distance computations between points on the surface of the Earth, including in the ocean, particularly for large-scale problems in oceanography. Because of the curvature of the Earth, the plane geometry is not applicable.

In this paper telegraph processes on geodesic lines of the Poincaré half-space and Poincaré disk are introduced and the behavior of their hyperbolic distances examined. Explicit distributions of the processes are obtained and the related governing equations derived. By means of the processes on geodesic lines, planar random motions (with independent components) in the Poincaré half-space and disk are defined and their hyperbolic random distances studied. The limiting case of one-dimensional and planar motions together with their hyperbolic distances is discussed with the aim of establishing connections with the well-known stochastic representations of hyperbolic Brownian motion. Extensions of motions with finite velocity to the three-dimensional space are also hinted at, in the final section.

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7 - Spherical Trigonometry and Distance Computation

Summary

Random motions at finite velocity in a non-Euclidean space

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2 results

7 - Spherical Trigonometry and Distance Computation

Summary

Random motions at finite velocity in a non-Euclidean space