The Velocity Tensor and the Momentum Tensor

TL;DR

This paper introduces the momentum tensor and explores its relationship with the velocity tensor, establishing a tensorial framework for classical and relativistic mechanics, primarily in two dimensions but applicable to higher dimensions.

Contribution

It presents the momentum tensor as a new fundamental object and analyzes its properties and relation to the velocity tensor within a tensorial mechanics framework.

Findings

Defines the momentum tensor and its properties

Establishes the relation between momentum and velocity tensors

Provides insights applicable to higher-dimensional spacetimes

Abstract

This paper introduces a new object called the momentum tensor. Together with the velocity tensor it forms a basis for establishing the tensorial picture of classical and relativistic mechanics. Some properties of the momentum tensor are derived as well as its relation with the velocity tensor. For the sake of clarity only two-dimensional case is investigated. However, general conclusions are also valid for higher dimensional spacetimes.