Multi-body Dynamics Modeling of Fixed-Pitch Coaxial Rotor Helicopter

Satoshi Suzuki, Takahiro Ishii, Gennai Yanagisawa, Kazuki Tomita, Yasutoshi Yokoyama


In this study, a mathematical model of a fixed-pitch co-axial rotor unmanned helicopter is derived by using a multi-body dynamics modeling technique. First, we consider the helicopter as a rigid body system which consists of 2 rigid bodies. The velocity transformation method, which is one of the multi body dynamics technique, is applied to derive equation of motion of the helicopter. All the forces and moments impressed into the helicopter are derived in consideration of the aerodynamics of co-axial rotors. Derived mathematical model of the helicopter is verified by comparing the flight experiment data with model output. Finally, fundamental motion analysis using the model is conducted to establish the motion characteristics of the helicopter.


co-axial rotor helicopter; multi-body dynamics modeling motion analysis.

Full Text:



B. Mettler, M. B. Tischler, and T. Kanade, “System Identification Modeling of A Small Scale Unmanned Rotorcraft for Flight Control Design,” Journal of American Helicopter Society, vol. 47, no. 1, 2002, pp. 50–63.

J. H. Lee, B. M. Min, and E. T. Kim, “Autopilot Design of Tilt-Rotor UAV using Particle Swarm Optimization Method,” Proceedings of 2007 International Conference on Control, Automation and Systems, 2007, pp. 1629–1633.

C. Bermes, S. Leutenegger, S. Bouabdallah, D. Schafroth, and R. Siegwart, “New Design of The Steering Mechanism for a Mini Coaxial Helicopter,” Proceedings of IEEE International Conference on Intelligent Robots and Systems, 2008, pp. 1236-1241.

S. Shen, N. Michael, and V. Kumar, “Autonomous Milti-Floor Indoor Navigation with A Computationally Constrained MAV,” Proceedings of IEEE International Conference on Robotics and Automation, 2011, pp. 20-25

T. Ishii, S. Suzuki, G. Yanagisawa, K. Tomita, Y. Yokoyama, “Multi-Body Dynamics Modeling of Fixed-pitch Co-axial Rotor Unmanned Helicopter,” Proceedings of International Conference on Intellignent Unmanned Systems 2011, 2011

H. Tajima, Fundamental of Multibody Dynamics, Tokyo Denki University Press, 2006, (in Japanese)

A. A. Shabana, Dynamics of Multibody Systems 3rd Edition, Cambridge, 2005

W. Jekkovsky, “The Structure of Multibody Dydnamics Equations,” Journal of Guidance and Control, vol. 1, no. 3, 1978, pp. 173-182

S. S. Kim, and M. J. Vanderploeg, “A General and Efficent Method for Dynamics Analysis of Mechanical System Using Velocity Transformation,” ASME Journal of Mechanisms, Transmissions, and Automation Design, vol. 108, 1986, pp. 176-182

A. R. S. Bramwell, G. Done, and D. Balmford, Bramwell’s Helicopter Dynamics, AIAA, 2001

H. Glauert, A General Theory of the Autogyro, Aeronautical Research Council R&M 1111, 1926



Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.