Minimum time loop maneuver with no speed loss

A problem of how to move the center of gravity of the maneuverable aircraft from one given point in the three-dimensional space to another point as quickly as possible with the fixed vectors of the respective velocities is considered. Numerical solutions for coinciding initial and final conditions f...

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Bibliographic Details
Published in:Journal of computer & systems sciences international 2012-11, Vol.51 (6), p.833-848
Main Authors: Zhelnin, Yu. N., Utemov, A. E., Shmatkov, A. M.
Format: Article
Language:English
Subjects:
Aircraft
Analysis
Aviation
Center of gravity
Control
Control algorithms
Control Systems of Moving Objects
Control theory
Curvature
Energy consumption
Engineering
Gravity
Mathematical analysis
Mathematical models
Mechatronics
Optimization
Pilots
Robotics
Studies
Three dimensional
Trajectories
Vectors (mathematics)
Velocity
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Summary:A problem of how to move the center of gravity of the maneuverable aircraft from one given point in the three-dimensional space to another point as quickly as possible with the fixed vectors of the respective velocities is considered. Numerical solutions for coinciding initial and final conditions for trajectories entirely lying in the vertical plane are found. The solution is shown to be non-unique in the general case, with the change of the sign of curvature of the best trajectory being possible. Locally optimal solutions are found. The problem that takes into account the restriction on the sign of curvature of the trajectory is considered, with the respective optimal controls obtained both for fixed and free end point. Examples are given for cases when the velocity vector equals the initial one at the end of motion.
ISSN:1064-2307
1555-6530
DOI:10.1134/S1064230712060160