کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4605991 | 1337673 | 2014 | 16 صفحه PDF | دانلود رایگان |
We research the Zermelo navigation problem on Riemannian manifolds in dim(R×M)=3dim(R×M)=3 under the force representing the action of the perturbing “wind” distribution modeled by the vector field on manifold M . We consider a fibered manifold π:R×M→Rπ:R×M→R where M represents the “sea”, RR represents the time and π is the first canonical projection. We perturb it by a time-(in)dependent vector field on the manifold M with a codimension one foliation. We aim to research the behavior of the paths in reference to their optimization. Geometrically we find the deviation of geodesics under the action of a time-dependent vector field. We present corresponding simulation with the whirlpool perturbation. We also consider a new concept of real application in the navigational decision support systems.
Journal: Differential Geometry and its Applications - Volume 35, Supplement, September 2014, Pages 334–349