On the invariant integration of a vector in some problems in mechanics

On the invariant integration of a vector in some problems in mechanics

Invariant integration of vectors and tensors over manifolds was introduced around fifty years ago by V.N. Folomeshkin, though the concept has not attracted much attention among researchers. Although it is a sophisticated concept, the operation of the invariant integration of vectors is actually requ...

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Veröffentlicht in:arXiv.org 2024-12
1. Verfasser: Saad Bin Mansoor
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Cartesian coordinates
Euclidean geometry
Invariants
Mechanics (physics)
Polar coordinates
Tensors
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description Invariant integration of vectors and tensors over manifolds was introduced around fifty years ago by V.N. Folomeshkin, though the concept has not attracted much attention among researchers. Although it is a sophisticated concept, the operation of the invariant integration of vectors is actually required to correctly solve some problems in mechanics. Two such problems are discussed in the present exposition, in the context of a two-dimensional Euclidean space covered by a polar coordinate system. The notion of invariant integration becomes necessary when the space is described without any reference to a Cartesian coordinate system.
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subjects Cartesian coordinates
Euclidean geometry
Invariants
Mechanics (physics)
Polar coordinates
Tensors
title On the invariant integration of a vector in some problems in mechanics
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