Galilean geometry of motions
Mehdi Nadjafikhah, Ahmad-Reza Forough
TL;DR
This paper demonstrates that the Galilean group forms a matrix Lie group, analyzes its structure, and identifies invariants of Galilean motions using Olver's moving coframes method, establishing a detailed geometric framework.
Contribution
It introduces the matrix Lie group structure of the Galilean group and applies Olver's method to find invariants and the e-structure of Galilean motions, advancing geometric understanding.
Findings
Galilean group is a matrix Lie group
Invariants of Galilean geometry are identified
e-structure of Galilean motions is derived
Abstract
In this paper we show that Galilean group is a matrix Lie group and find its structure. Then provide the invariants of special Galilean geometry of motions, by Olver's method of moving coframes, we also find the corresponding structure.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematics and Applications · Robotic Mechanisms and Dynamics · Control and Dynamics of Mobile Robots