Mathematics (Oct 2021)

Lie-Group Modeling and Numerical Simulation of a Helicopter

  • Alessandro Tarsi,
  • Simone Fiori

DOI
https://doi.org/10.3390/math9212682
Journal volume & issue
Vol. 9, no. 21
p. 2682

Abstract

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Helicopters are extraordinarily complex mechanisms. Such complexity makes it difficult to model, simulate and pilot a helicopter. The present paper proposes a mathematical model of a fantail helicopter type based on Lie-group theory. The present paper first recalls the Lagrange–d’Alembert–Pontryagin principle to describe the dynamics of a multi-part object, and subsequently applies such principle to describe the motion of a helicopter in space. A good part of the paper is devoted to the numerical simulation of the motion of a helicopter, which was obtained through a dedicated numerical method. Numerical simulation was based on a series of values for the many parameters involved in the mathematical model carefully inferred from the available technical literature.

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