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# 04, April 2012
77-30569/280337 Approximation of the segment of dynamically controlled system flat movement trajectory with the usage of logarithmic spiral.
Engineering Education # 11, November 2011
Description of dynamically controlled object flat trajectory with piecewise constant plots of control was obtained with use of logarithmic spiral plot. Examples of the segments of acceleration and deceleration with fixed values of normal and tangent overloads were included in the article. The usage of this approximation method for models moving along the flat trajectories allows to substitute system of differential equations with analytical dependences.  That technique leads to significant reduce in trajectory creation time.
77-30569/280579 Knapsack problem solving procedure in the case of boundaries vector
Engineering Education # 12, December 2011
Modification of classical method of solving the knapsack problem as the task of bivalent programming in the case of boundaries vector is proposed. Algorithm of knapsack acquisition problem solving in the case of one criteria and vector of boundaries is presented. Problems of solution existence and optimality solution check are considered. An example of the problem solving on the basis of proposed method is given.
77-30569/280873 Trajectory safety ensuring for the problem of fly-around of dynamic circle zone
Engineering Education # 12, December 2011
The problem of trajectory safety ensuring for the dynamic controlled object (DCO) that moves on a plane in which circle forbidden zone exists is considered. Mathematical model of DCO motion is described. At first the case of static circle forbidden zone is considered for the formalization of the fly-around problem, intervals of non-safety courses of motion which form a zone of dangerous trajectories for the class of piecewise path segments of motion consisting of trajectory of sharp turn of the maximum curvature and linear path segment after it. Problem of evaluation of the zone of dangerous trajectories in the case of dynamic circle forbidden zone is considered on the basis of the obtained description. As a result iteration algorithm of the zone of dangerous trajectories evaluation is formed.
 
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