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

Romano, Marcello

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

dc.contributor.author	Romano, Marcello
dc.contributor.corporate	Naval Postgraduate School (U.S.)
dc.contributor.department	Mechanical & Astronautical Engineering
dc.date.accessioned	2014-04-07T18:43:03Z
dc.date.available	2014-04-07T18:43:03Z
dc.date.issued	2008-01-31
dc.description	The article of record as published may be found at: http://dx.doi.org/10.1007/s10569-007-9112-7	en_US
dc.description	"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.)	en_US
dc.description.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.	en_US
dc.identifier.citation	Celestial Mech. Dyn. Astr., v. 100, (2008), pp. 181-189
dc.identifier.uri	https://hdl.handle.net/10945/40276
dc.publisher	Springer
dc.rights	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.
dc.subject.author	rigid body dynamics	en_US
dc.subject.author	kinematics	en_US
dc.subject.author	rotation	en_US
dc.subject.author	integrable cases of motion	en_US
dc.subject.author	spherical ellipsoid of inertia	en_US
dc.title	Exact analytic solution for the rotation of a rigid body having spherical ellipsoid of inertia and subjected to a constant torque	en_US
dc.type	Article
dspace.entity.type	Publication