The flow of the Euler top is a geodesic flow on SO(3) with a left invariant metric. We determine the conjugate locus for this geodesic flow in the case that the metric has an S1 invariance, which is the case when two of the three moments of inertia are equal. Depending on the ratios of these moments, the conjugate locus is either a segment or circle (if the body is oblate) or a non–injective mapping of an astroid of revolution (if the body is prolate).
The conjugate locus for the Euler top. I. The axisymmetric case
FASSO', FRANCESCO
2007
Abstract
The flow of the Euler top is a geodesic flow on SO(3) with a left invariant metric. We determine the conjugate locus for this geodesic flow in the case that the metric has an S1 invariance, which is the case when two of the three moments of inertia are equal. Depending on the ratios of these moments, the conjugate locus is either a segment or circle (if the body is oblate) or a non–injective mapping of an astroid of revolution (if the body is prolate).
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