Some rational vehicle motions

Jon Selig

doi:10.1007/978-94-007-7214-4-3

Some rational vehicle motions

Jon Selig

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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. © Springer Science+Business Media Dordrecht 2014.

Original language	English
Title of host publication	Computational Kinematics Proceedings of the 6th International Workshop on Computational Kinematics (CK2013)
Publisher	Springer
Pages	21 - 29
DOIs	https://doi.org/10.1007/978-94-007-7214-4-3
Publication status	Published - 12 May 2013
Externally published	Yes

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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. {\textcopyright} Springer Science+Business Media Dordrecht 2014.",

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AB - 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. © Springer Science+Business Media Dordrecht 2014.

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M3 - Chapter

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BT - Computational Kinematics Proceedings of the 6th International Workshop on Computational Kinematics (CK2013)

PB - Springer

ER -

Some rational vehicle motions

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