Abstract
In this paper, the stationary acceleration of the spherical general helix in a 3-dimensional Lie group is studied by using a bi-invariant metric. The relationship between the Frenet elements of the stationary acceleration curve in 4-dimensional Euclidean space and the intrinsic Frenet elements of the Lie group is outlined. As a consequence, the corresponding curvature and torsion of these curves are computed. In Minkowski space, for the curves on a timelike surface to have a stationary acceleration, a necessary and sufficient condition is refined.
Highlights
Rigid body motion has attracted continuous attention since the time of Galileo and Bernoulli, and recently, the subject has generated a renewed interest in differential geometry
SE( ) is the space of all rigid body motions, and the motions can be described as curves in this space [ ]
It is proved that the normal curvature, geodesic curvature and geodesic torsion functions of the curves on a timelike surface in the Minkowsky space are linear
Summary
Rigid body motion has attracted continuous attention since the time of Galileo and Bernoulli, and recently, the subject has generated a renewed interest in differential geometry. By using the Serret-Frenet frame in a -dimensional Lie group with a bi-invariant metric, the stationary acceleration of the spherical general helix is studied.
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