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Exact Analytic Solutions for the Rotation of an Axially Symmetric Rigid Body Subjected to a Constant Torque
Full text link"Errata Corridge Postprint" version of the journal paper. The following typos present in the Journal version are HERE corrected: 1) Definition of \beta, before Eq. 18; 2) sign in the statement of Theorem 3; 3) Sign in Eq. 53; 4)Item r_0 in Eq. 58; 5) Item R_{SN}(0) in Eq. 62The article of record as published may be located at http://dx.doi.org/10.1007/s10569-008-9155-4New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are obtained for the following cases: (1) Torque parallel to the symmetry axis and arbitrary initial angular velocity; (2) Torque perpendicular to the symmetry axis and such that the torque is rotating at a constant rate about the symmetry axis, and arbitrary initial angular velocity; (3) Torque and initial angular velocity perpendicular to the symmetry axis, with the torque being fixed with the body. In addition to the solutions for these three forced cases, an original solution is introduced for the case of torque-free motion, which is simpler than the classical solution as regards its derivation and uses the rotation matrix in order to describe the body orientation. This paper builds upon the recently discovered exact solution for the motion of a rigid body with a spherical ellipsoid of inertia. In particular, by following Hestenes' theory, the rotational motion of an axially symmetric rigid body is seen at any instant in time as the combination of the motion of a "virtual" spherical body with respect to the inertial frame and the motion of the axially symmetric body with respect to this "virtual" body. The kinematic solutions are presented in terms of the rotation matrix. The newly found exact analytic solutions are valid for any motion time length and rotation amplitude. The present paper adds further elements to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists
New species and new records of mutillid wasps from the Socotra Archipelago (Hymenoptera: Mutillidae)
No full textCascio, Pietro Lo, Romano, Marcello, Grita, Flavia (2012): New species and new records of mutillid wasps from the Socotra Archipelago (Hymenoptera: Mutillidae). Acta Entomologica Musei Nationalis Pragae 52: 525-544, DOI: 10.5281/zenodo.534029
Exact analytic solution for the rotation of a rigid body having spherical ellipsoid of inertia and subjected to a constant torque
Full text linkThe 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.)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
Fig. 15 in New species and new records of mutillid wasps from the Socotra Archipelago (Hymenoptera: Mutillidae)
No full textFig. 15. Habitus of Dentilla socotrana sp. nov. (holotype) in dorsal and lateral view. Scale bar = 1 mm.Published as part of Cascio, Pietro Lo, Romano, Marcello & Grita, Flavia, 2012, New species and new records of mutillid wasps from the Socotra Archipelago (Hymenoptera: Mutillidae), pp. 525-544 in Acta Entomologica Musei Nationalis Pragae 52 on page 540, DOI: 10.5281/zenodo.534029
A 4-PI steradians dynamic three-axis simulator for satellite hardware-in-the-loop experiments
No full text
Detumbling and nutation canceling maneuvers with complete analytic reduction for axially symmetric spacecraft
Full text linkThe article of record as published may be located at http://dx.doi.org/10.1016/j.actaastro.2009.09.015A new method is introduced to control and analyze the rotational motion of anaxially
symmetric rigid-body spacecraft. In particular, this motion is seen as the combination of
the rotation of a virtual sphere with respect to the inertial frame, and the rotation of the
body, about its symmetry axis, with respect to this sphere. Two new exact solutions are
introduced for the motion of axially symmetric rigid bodies subjected to a constant
external torque in the following cases: (1) torque parallel to the angular momentum and
(2) torque parallel to the vectorial component of the angular momentum on the plane
perpendicular to the symmetry axis. By building upon these results, two rotational
maneuvers are proposed for axially symmetric spacecraft: a detumbling maneuver and
a nutation canceling maneuver. The two maneuvers are the minimum time maneuvers
for spherically constrained maximum torque. These maneuvers are simple and elegant,
as they reduce the control of the three degrees-of-freedom nonlinear rotational motion
to a single degree-of-freedom linear problem. Furthermore, the complete (both for the
dynamics and for the kinematics) and exact analytic solutions are found for the two
maneuvers. An extended survey is reported in the introduction of the paper of the few
cases where the rotation of a rigid body is fully reduced to an exact analytic solution in
closed form
New Families of Halo Orbits about the Photo-Gravitational Equilibrium in the Sun-Earth-Moon System’s Center of Mass Elliptic Restricted Three-Body Problem for Planetary Sunshade Missions
No full textThis paper investigates halo orbits about the photo-gravitational equilibrium point L1 between Sun and
the center of mass of the Earth–Moon system. In a previous paper, the authors discussed the existence
of suitable orbits for Planetary Sunshade missions in the photo-gravitational Sun - Earth–Moon system’s
center of mass Circular Restricted Three Body Problem with solar radiation pressure acting on perfectly
reflecting solar-sails satellites [C. L. Matonti, E. Scantamburlo, M. Romano, New Families of Halo
Orbits about the Photo-Gravitational Equilibrium between Sun and the Earth–Moon System for Planetary
Sunshade Missions, 74th International Astronautical Congress, Baku, 2023]. In this paper, a higher fidelity
model is considered. In particular, the orbital mechanics is modeled according to the corresponding
photo-gravitational Sun - Earth–Moon system’s center of mass Elliptic Restricted Three Body Problem.
Furthermore, the solar pressure force is now modeled by considering the reflectance, absorption and
emissivity of the surface of a non-ideal solar-sail satellite. Families of new orbits are found by using the
above model. The newly introduced orbits could be utilized by a swarm of solar-sail satellites to implement
a dynamic Planetary Sunshade System for Earth’s climate-change mitigation. This dynamic Planetary
Sunshade System acts as a space-based geoengineering infrastructure whose aim is to reduce part of the
oncoming solar radiance. In particular, for each of those families (proposed for the first time to the best
knowledge of the authors), the orbits lie on different planes or cylinders, and the projection of the satellites’
sails covers a circle. That circle resides on a plane perpendicular to the line joining the Sun center and
the Earth–Moon system’s center of mass. The orbit of each satellite was found by choosing the analytical
expression of a periodic trajectory in that plane, and by computing the initial condition that enables a closed
orbit in three dimensions. The needed continuous control force, on each solar-sail satellites, exploits the
solar-radiation pressure acceleration, which is modeled with two components tangential and perpendicular
to the sail. The direction of the control force is varied by controlling the satellite’s orientation about
two axes. The control angles expressions were found for each satellite’s orientation history. The orbital
stability of each of those families is finally discussed
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