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Geometric Pseudospectral Method on SE(3) for Rigid-Body Dynamics with Application to Aircraft
Joint Authors
Shen, Lincheng
An, Honglei
Li, Jie
Zhu, Huayong
Fang, Bin
Source
Mathematical Problems in Engineering
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-04-28
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
General pseudospectral method is extended to the special Euclidean group SE(3) by virtue of equivariant map for rigid-body dynamics of the aircraft.
On SE(3), a complete left invariant rigid-body dynamics model of the aircraft in body-fixed frame is established, including configuration model and velocity model.
For the left invariance of the configuration model, equivalent Lie algebra equation corresponding to the configuration equation is derived based on the left-trivialized tangent of local coordinate map, and the top eight orders truncated Magnus series expansion with its coefficients of the solution of the equivalent Lie algebra equation are given.
A numerical method called geometric pseudospectral method is developed, which, respectively, computes configurations and velocities at the collocation points and the endpoint based on two different collocation strategies.
Through numerical tests on a free-floating rigid-body dynamics compared with several same order classical methods in Euclidean space and Lie group, it is found that the proposed method has higher accuracy, satisfying computational efficiency, stable Lie group structural conservativeness.
Finally, how to apply the previous discretization scheme to rigid-body dynamics simulation and control of the aircraft is illustrated.
American Psychological Association (APA)
Li, Jie& An, Honglei& Zhu, Huayong& Shen, Lincheng& Fang, Bin. 2013. Geometric Pseudospectral Method on SE(3) for Rigid-Body Dynamics with Application to Aircraft. Mathematical Problems in Engineering،Vol. 2013, no. 2013, pp.1-16.
https://search.emarefa.net/detail/BIM-1032007
Modern Language Association (MLA)
Li, Jie…[et al.]. Geometric Pseudospectral Method on SE(3) for Rigid-Body Dynamics with Application to Aircraft. Mathematical Problems in Engineering No. 2013 (2013), pp.1-16.
https://search.emarefa.net/detail/BIM-1032007
American Medical Association (AMA)
Li, Jie& An, Honglei& Zhu, Huayong& Shen, Lincheng& Fang, Bin. Geometric Pseudospectral Method on SE(3) for Rigid-Body Dynamics with Application to Aircraft. Mathematical Problems in Engineering. 2013. Vol. 2013, no. 2013, pp.1-16.
https://search.emarefa.net/detail/BIM-1032007
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1032007