Abstract
It is observed that the kinematic equations of many vehicles take the same form. This form is that the body-fixed velocity twist of the vehicle lies in a fixed screw-system of a particular type. The Cayley map can be used to pull-back these equations to the Lie algebra of the group of rigid-body motions. Rational solutions to the equations can be found by the method of undetermined coefficients. Since the Cayley map is a rational map, mapping these rational solutions back to the group gives rational rigid-body motions. A 3-parameter family of rational Frenet-Serret motions is found in this way. Multiplying these motions by a rational roll-motion gives a 4-parameter family of aeroplane motions.
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This work was has been much improved following the comment of the anonymous reviewers.
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Selig, J.M. (2014). Some Rational Vehicle Motions. In: Thomas, F., Perez Gracia, A. (eds) Computational Kinematics. Mechanisms and Machine Science, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7214-4_3
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DOI: https://doi.org/10.1007/978-94-007-7214-4_3
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