What is it about?
This paper is derived from a work we presented at the AHS forum. The title was: "Do We Really Need To Study Rotorcraft as Linear Periodic Systems?" The implicit answer is: "no". Indeed, we can remove most of the simplifying assumptions usually made when studying the stability of rotorcraft: not just linearity, but also periodicity, and still be able to capture the essence of perturbed motion in the vicinity of a loose reference trajectory. Of course, this approach is a bit more computationally intensive, but perfectly affordable, nowadays...
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Why is it important?
It took about 100 years to make one of many Lyapunov's intuitions practically computable. Surprisingly, it took another 35 years before it was applied to rotorcraft stability, possibly one of the most suitable case studies for Lyapunov exponents. We believe this method can be as revolutionary for rotorcraft as Floquet's was nearly 40 years ago.
Perspectives
I believe there is a lot of potential in Lyapunov exponents applied to rotorcraft aeromechanics. We are just at the beginning of the exploration.
Professor Pierangelo Masarati
Politecnico di Milano
Read the Original
This page is a summary of: Stability of Nonlinear, Time-Dependent Rotorcraft Systems Using Lyapunov Characteristic Exponents, Journal of the American Helicopter Society, April 2016, American Helicopter Society,
DOI: 10.4050/jahs.61.022003.
You can read the full text:
Resources
Estimation of Lyapunov Exponents from Multibody Dynamics in Differential-Algebraic Form
P. Masarati, "Estimation of Lyapunov Exponents from Multibody Dynamics in Differential-Algebraic Form", Proc. IMechE Part K: J. Multi-body Dynamics 227(1):23-33, March 2013, doi:10.1177/1464419312455754.
Sensitivity of Trajectory Stability Estimated by Lyapunov Characteristic Exponents
P. Masarati, A. Tamer, "Sensitivity of Trajectory Stability Estimated by Lyapunov Characteristic Exponents", Aerospace Science and Technology, 47:501-510, December 2015, doi:10.1016/j.ast.2015.10.015.
The Real Schur Decomposition Estimates Lyapunov Characteristic Exponents With Multiplicity Greater Than One
P. Masarati, A. Tamer, "The Real Schur Decomposition Estimates Lyapunov Characteristic Exponents With Multiplicity Greater Than One", Proc. IMechE Part K: J. Multi-body Dynamics, 230(4):568-578, December 2016, doi:10.1177/1464419316637275.
Contributors
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