Choice of Riemannian Metrics for Rigid Body Kinematics
نویسندگان
چکیده
The set of spatial rigid body motions forms a Lie group known as the special Euclidean group in three dimensions, (3). Chasles’s theorem states that there exists a screw motion between two arbitrary elements of (3). In this paper we investigate whether there exist a Riemannian metric whose geodesics are screw motions. We prove that no Riemannian metric with such geodesics exists and we show that the metrics whose geodesicsare screw motions form a two-parameter family of semi-Riemannian metrics.
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تاریخ انتشار 2013