New State Transition Matrices for Spacecraft Relative Motion in Perturbed Orbits

2017 ◽  
Vol 40 (7) ◽  
pp. 1749-1768 ◽  
Author(s):  
Adam W. Koenig ◽  
Tommaso Guffanti ◽  
Simone D’Amico
Keyword(s):  
Relative Motion ◽  
State Transition ◽  
Transition Matrices

A formal semantics of extended hierarchical state transition matrices using CSP#

2013 ◽  
Vol 26 (5) ◽  
pp. 943-962 ◽  
Author(s):  
Yoriyuki Yamagata ◽  
Weiqiang Kong ◽  
Akira Fukuda ◽  
Nguyen Van Tang ◽  
Hitoshi Ohsaki ◽  
...  
Keyword(s):  
State Transition ◽  
Formal Semantics ◽  
Transition Matrices

On Instability Pockets and Influence of Damping in Parametrically Excited Systems

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Ashu Sharma ◽  
S. C. Sinha
Keyword(s):  
Degrees Of Freedom ◽  
State Transition ◽  
Degree Of Freedom ◽  
Transition Matrices ◽  
Stability Boundaries ◽  
Parametrically Excited ◽  
Parametric Space ◽  
Stability Diagrams ◽  
Wide Range ◽  
The Stability

In most parametrically excited systems, stability boundaries cross each other at several points to form closed unstable subregions commonly known as “instability pockets.” The first aspect of this study explores some general characteristics of these instability pockets and their structural modifications in the parametric space as damping is induced in the system. Second, the possible destabilization of undamped systems due to addition of damping in parametrically excited systems has been investigated. The study is restricted to single degree-of-freedom systems that can be modeled by Hill and quasi-periodic (QP) Hill equations. Three typical cases of Hill equation, e.g., Mathieu, Meissner, and three-frequency Hill equations, are analyzed. State transition matrices of these equations are computed symbolically/analytically over a wide range of system parameters and instability pockets are observed in the stability diagrams of Meissner, three-frequency Hill, and QP Hill equations. Locations of the intersections of stability boundaries (commonly known as coexistence points) are determined using the property that two linearly independent solutions coexist at these intersections. For Meissner equation, with a square wave coefficient, analytical expressions are constructed to compute the number and locations of the instability pockets. In the second part of the study, the symbolic/analytic forms of state transition matrices are used to compute the minimum values of damping coefficients required for instability pockets to vanish from the parametric space. The phenomenon of destabilization due to damping, previously observed in systems with two degrees-of-freedom or higher, is also demonstrated in systems with one degree-of-freedom.

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