Publication:
Exact analytic solution for the rotation of a rigid body having spherical ellipsoid of inertia and subjected to a constant torque

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Authors
Romano, Marcello
Subjects
rigid body dynamics
kinematics
rotation
integrable cases of motion
spherical ellipsoid of inertia
Advisors
Date of Issue
2008-01-31
Date
Publisher
Springer
Language
Abstract
The exact analytic solution is introduced for the rotational motion of a rigid body having three equal principal moments of inertia and subjected to an external torque velocity which is constant for an observer fixed with the body, and to arbitrary initial angular velocity. In the paper a parametrization of the rotation by three complex numbers is used. In particular, the rows of the rotation matrix are seen as elements of the unit sphere and projected, by stereographic projection, onto points on the complex plane. In this representation, the kinematic differential equation reduces to an equation of Riccati type, which is solved through appropriate choices of substitutions, thereby yielding an analytic solution in terms of confluent hypergeometric functions. The rotation matrix is recovered from the three complex rotations variables by inverse stereographic map. The results of a numerical experiment confirming the exactness of the analytic solution are reported. The newly found analytic solution is valid for any motion time length and rotation amplitude. The present paper adds a further element to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.
Type
Article
Description
The article of record as published may be found at: http://dx.doi.org/10.1007/s10569-007-9112-7
"ERRATA CORRIDGE POSTPRINT" of the following paper: Celestial Mech Dyn Astr (2008) 100:181-189 Noname manuscript No. (will be inserted by the editor) DOI: 10.1007/s10569-007-9112-7 (In particular: types present in Eq. 28 of the Journal version are HERE corrected.)
Series/Report No
Department
Mechanical & Astronautical Engineering
Organization
Naval Postgraduate School, Monterey, California
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NPS Report Number
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Format
Citation
Celestial Mech. Dyn. Astr., v. 100, (2008), pp. 181-189
Distribution Statement
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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