Dr. Daniele Mortari is Associate Professor of Aerospace Engineering at Texas A&M University in College Station, working on the field of spacecraft dynamics and control. During his 25-year career as an educator and researcher, he has made contributions to his field in two key areas of specialization: spacecraft attitude estimation and spacecraft formation design. In addition to Texas A&M University, Dr. Mortari has taught at the Aerospace Engineering School of Rome’s University and at Electronic Engineering of Perugia’s University, Italy. He is Associate Editor for AAS Journal of the Astronautical Sciences, for the International Journal of Navigation and Observations, and for IEEE Transactions on Aerospace and Electronic Systems. Dr. Mortari is AIAA Associate Fellow and member of Space Flight Mechanics Technical Committee. He received his "Dottore" degree in Nuclear Engineering from the Rome’s University "La Sapienza," Italy. He has published extensively on the topics of his study, holds multiple U.S. patents and has been widely recognized for his work, including receiving two NASA’s Group Achievement award, the 2003 Spacecraft Technology Center award, and the 2007 IEEE Judith A. Resnik award.

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Tel: +1 (979) 845-0734
Fax: +1 (979) 845-6051
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Tutorial:

Flower Constellations in Aerospace Engineering

Flower Constellations (FC) are a new and revolutionary methodology to design satellite constellations discovered at Texas A&M University in 2004 by Mortari and his two PhD students, Wilkins and Bruccoleri. The theory, which has not been fully completed yet, has been derived from the theory of compatible (or resonant) orbits. Like the wagons of a train, the satellites of a FC all run along a common trajectory as seen from a rotating reference frame. This is the result of a 3-Dimensional "space juggling" that makes the satellites describe unique relative dynamics. These dynamics allow the design of constellations in which the satellites can be:

1) time-uniformly distributed, that is, as observed from a reference rotating frame (e.g., the Earth), subsequent satellite passages occur at constant time interval;
2) space-uniform distributed, that is, as for repulsive charges, satellites are displaced one from another with maximum distance; and
3) persistently observing specific regions, that is, the juggling of the FC satellites is such that, as a satellite leaves a geographical region of interest, a new satellite enters into the region with a continuous and natural synchronization.

The above capabilities are very important for many applications, often coinciding with the optimality definitions. However, the most surprising product of the FC (and what makes the theory unique) is the capability of producing harmonic FC. These are new (and unexpected) time-invariant space "objects". The satellites of harmonic FC are distributed to form 3-D figures (e.g., square, circle, star, helix, shield, etc.) whose shapes are preserved during the dynamics, as if they were rigid! No control (other than compensation for perturbations) is required to maintain these configurations. The shape invariance is naturally obtained by synchronized dynamics. This is a truly fundamental breakthrough in satellite orbit technology waiting for future applications.

Flower Constellations can be seen as new space objects that can be shaped by playing with the FC design parameters. These objects are axial-symmetric objects spinning with prescribed angular velocity about the axis of symmetry which can be aligned to any direction in space. As a very important case, when the FC axis of symmetry is aligned with the Earth's spin axis, the perturbations due to the Earth oblateness are identical for all orbits. Consequently, the satellite juggling (phasing) does not change and therefore the object axial-symmetric shape is preserved. The mathematics involved in describing FC mainly pertains to number theory, since the main design parameters are integers.

Recently, it has been recognized that the dynamics and the shapes of FC can be found in nature. Crystals, flowers, plants, dynamics of electrons, and molecules often reflect shapes of FC. For this reason an important part of this research is to find potential connections of the FC theory with areas outside aerospace engineering as for instance, chemistry, science, and physics.