Chaotic Attitude Motion of Symmetric Gyrostat via Melnikov Integral
by
Jinlu Kuang
SEC, School of EEE, Nanyang Technological University, Singapore 639798
Coauthors: Soonhie TAN (School of EEE, Nanyang Technological University, Singapore 639798), K. Arichandran (School of EEE, Nanyang Technological University, Singapore 639798)

In this paper are derived the Hamiltonian equations of attitude motions for the gyrostat of six degrees of freedom by using the Deprit's variables. The moment of momentum of the wheels inside is assumed to be constants along the body-fixed axes. Using the theory of elliptic functions the torque-free homoclinic solutions of the Kelvin symmetric gyrostat are obtained analytically. Employing the Melnikov integral the concrete version of Melnikov function is formulated as the condition for the occurrance of attitude chaos. Based upon the derived Melnikov function, the bifurcation curves are computed. By using the fourth-order Runge-Kutta integral scheme, the attitude steady-state behaviour is numerically exhibited with the help of phase portraits which show that there are a lot of random motion possessing a non-periodic solution.

Date received: December 29, 1999