Eduardo PolliPolitecnico di Milano | Polimi · Department of Aerospace Engineering
Eduardo Polli
Master of Engineering
Mission Design
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Introduction
Publications
Publications (4)
This works presents an optimal control direct method to design fuel-optimal low-thrust Collision Avoidance Manoeuvres (CAMs), imposing return to nominal conditions and including eclipse constraints. The methodology exploits the Hermite-Simpon integration scheme to impose the dynamics and the Squared Mahalanobis Distance (SMD) to ensure a collision...
At a time when space debris are already a growing issue in the space sector, the deployment of large constellations, made of hundreds to thousands of satellites, is of concern from an environmental point of view. In the next decade, the space sector will undergo a considerable change as the population of active satellites is about to quintuple. Thi...
This paper presents an analytical model for collision probability assessments between de-orbiting or injecting space objects and satellite constellations. Considering the first to be subjected to a continuous tangential acceleration, its spiraling motion would result in a series of close approaches in the proximity of a constellation. The proposed...
An analytical model for collision probability assessments between de-orbiting or injecting space objects and satellite constellations is presented in this study. Considering the first to be subjected to a tangential acceleration, its spiral motion would result in a series of close approaches in the proximity of a constellation; in this work, a mode...
Questions
Questions (3)
I'm designing the feedback control of a CubeSat which shall always points towards the Sun.
For attitude determination I use a magnetometer and a Sun sensor while for control 8 cold gas thruster and 4 CMGs.
Since I need my Sat to point towards the Sun I wanted to use a Sun-synchronous orbit so that i don't need to consider eclipses.
Are there other orbits which i'm ignoring that might do the job even better?
Thanks in advance.
As an example, I'm considering a beam hinged at one end which is subjected to a prescribed angular velocity Omega. (EJ = bending stiffness , m = mass per unit length , l = length).
Let's assume i want to use Lagrange equations with a Ritz approx (Assumed modes method).
Kinetic energy:
T = 1/2 int_0^l ( s/t m s/t) dx
Potential energy:
K = 1/2 int_0^l (w/xx EJ w/xx) dx
where s/t indicates the derivative of s over time, s being the displacement of a general point of the beam. w is the bending displacement.
Now i would compute s in terms of the rigid angle of the beam theta and the bending displacement w, so s = s(x , theta , w).
Considering the beam in its initial position on the x-axis from x = 0 to x = l :
initial set of point P_0 = (x , w(x,t))
using rotation matrix R(theta) P_1 = R*P_0
s = P_1 - P_0
Now i would apply the Ritz approx to the displacement w with a trial function like N(x) = x/l ( hoping it is suitable).
and i have my equations of motion in the unknowns theta and w, where theta is the integral between 0 and t of the angular speed Omega.
Would this procedure be right? If not, how should I treat a problem like this one?
Hope I was clear enough, not easy without LaTeX.
Thank you
Considering a trivial LTI:
x' = Ax + Bu
y = Cx + Du
I was told that from this representation I can always derive a model without the direct feedthourgh matrix D in order to solve Lyapunov equation.
I was trying to do this by including the input vector u inside the state vector x, but i can't understand how.
What is the classical approach to this problem?
