Kinematic Comparison of Exponential and Cayley Maps in the Planar Motion Group

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International Electronic Journal of Geometry
Volume:13 Issue:1
Kinematic Comparison of Exponential and Cayley Maps in the Planar Motion Group

Kinematic Comparison of Exponential and Cayley Maps in the Planar Motion Group

Authors : İlhan KARAKILIÇ, Soner ERKUŞ

Pages : 107-115

Doi:10.36890/iejg.699429

View : 57 | Download : 11

Publication Date : 2020-01-30

Article Type : Research Paper

Abstract :In this work, the exponential and the Cayley maps, from the Lie algebra $\mathfrak{seinsert ignore into journalissuearticles values(2);}$ of the planar motion group $SEinsert ignore into journalissuearticles values(2);$, to the group itself are studied. The comparison between these maps on $SEinsert ignore into journalissuearticles values(2);$ is given by using the Rodrigues vector. A three joint mechanism is discussed as an application.
Keywords : Kinematics, Lie Group, planar motion group, exponential map, Cayley map, Rodrigues vector

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