Nonlinearity index of the cayley form

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Nonlinearity index of the cayley form

Nonlinearity index of the cayley form

Sinclair, Andrew J. / Hurtado, John E. / Junkins, John L.

Abstract The nonlinearity index is a measure of the nonlinearity of dynamical systems based on computing the initial-condition sensitivity of the state-transition matrix. The Cayley form is a representation for dynamical systems that relates their motion to N-dimensional rotations. The generalized coordinates of the system are used to define an N-dimensional orientation, and a set of quasi velocities is defined equal to the corresponding angular velocity. The nonlinearity index of the Cayley-form representation is computed for an elastic spherical pendulum and a planar satellite example. These results are compared to values for alternative dynamical representations. Additionally, the nonlinearity is evaluated by analyzing how well the linearized equations of each representation capture certain properties of the motion. These results show that the Cayley form can have lower nonlinearity than traditional representations, in particular those representations that suffer from kinematic singularities.

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Title :

Nonlinearity index of the cayley form

Contributors:

Sinclair, Andrew J. (author) / Hurtado, John E. (author) / Junkins, John L. (author)

Published in:

The Journal of the Astronautical Sciences ; 54 , 3 ; 619-634

Publication date :

2006-12-01

Size :

16 pages

ISSN :

DOI :

https://doi.org/10.1007/BF03256509

Type of media :

Article (Journal)

Type of material :

Electronic Resource

Language :

English

Keywords :

Linearize Departure Equation , Kinematic Singularity , Nonlinearity Index , Nominal Trajectory , Neighboring Trajectory Engineering , Aerospace Technology and Astronautics , Mathematical Applications in the Physical Sciences , Extraterrestrial Physics, Space Sciences

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