Matsumoto Metrics Research Articles

Pure pursuit navigation on Riemannian manifolds

Here, the Pure Pursuit navigation on Riemannian manifolds is studied and the time optimal trajectories of this process are found. It has been shown that these trajectories are geodesics of a non-Randers type Finsler metric, known in the literature as Matsumoto metric. A geometrical approach to kinematics in control theory is illustrated and the inverse problem is formulated.

Projectively flat Matsumoto metric and its approximation

In this article, the author studies the projectively flat Matsumoto metric F = α 2/(α-β), where α = a i j y i y j is a Riemannian metric and β = b i y i is a 1-form. They conclude that α is locally projectively flat and β is paralled with respect to α. And get the same result for the higher order approximate Matsumoto metric.

Introduction to Matsumoto metric

Even though the notion of Matsumoto metric is quite an old topic, very few people took a close look into its true nature. In general, it is thought of as a particular case of the class of ( α , β ) -metrics with the variables α and β being independent. This is not exactly the case, as we shall see. In the present paper, we are going to reconsider the original meaning of the Matsumoto metric and study some of its fundamental properties from a new perspective.

PROJECTIVELY FLAT FINSLER SPACE WITH AN APPROXIMATE MATSUMOTO METRIC

The Matsumoto metric is an (fi;fl)-metric which is an exact formulation of the model of Finsler space. Lately, this metric was expressed as an infinite series form for jflj < jfij by the first author. He introduced an approximate Matsumoto metric as the (fi;fl)-metric of finite series form and investigated it in (11). The purpose of the present paper is devoted to finding the condition for a Finsler space with an approximate Matsumoto metric to be projectively flat.