*Article* **Lie-Group Modeling and Numerical Simulation of a Helicopter**

**Alessandro Tarsi <sup>1</sup> and Simone Fiori 2,\***


**Abstract:** 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.

**Keywords:** Lagrange–d'Alembert principle; non-conservative dynamical system; Euler–Poincaré equation; helicopter model; Lie group
