TY - JFULL
AU - Nemat Abazari and Ilgin Sager
PY - 2010/7/
TI - An Optimal Control Problem for Rigid Body Motions on Lie Group SO(2, 1)
T2 - International Journal of Mathematical and Computational Sciences
SP - 701
EP - 707
VL - 4
SN - 1307-6892
UR - https://publications.waset.org/pdf/5392
PU - World Academy of Science, Engineering and Technology
NX - Open Science Index 42, 2010
N2 - In this paper smooth trajectories are computed in the Lie group SO(2, 1) as a motion planning problem by assigning a Frenet frame to the rigid body system to optimize the cost function of the elastic energy which is spent to track a timelike curve in Minkowski space. A method is proposed to solve a motion planning problem that minimize the integral of the square norm of Darboux vector of a timelike curve. This method uses the coordinate free Maximum Principle of Optimal control and results in the theory of integrable Hamiltonian systems. The presence of several conversed quantities inherent in these Hamiltonian systems aids in the explicit computation of the rigid body motions.
ER -