C&SA | Contents

Volume 56 >>> № 5 SEPTEMBER — OCTOBER 2020

UDC 519.85

M.I. Gil¹, V.M. Patsuk²

¹ A. Pidgorny Institute of Mechanical Engineering Problems,
National Academy of Sciences of Ukraine, Kharkiv, Ukraine

² A. Pidgorny Institute of Mechanical Engineering Problems,
National Academy of Sciences of Ukraine, Kharkiv, Ukraine

PHI-FUNCTIONS OF 2D OBJECTS WITH BOUNDARIES BEING SECOND ORDER CURVES

Abstract. An approach to constructing analytical conditions of non-intersection and inclusion of non-oriented convex 2D objects is considered, the boundaries of objects being second-order curves in the canonical form. In particular, the conditions of mutual non-intersection of a pair of ellipses; an ellipse and an area bounded by a parabola; conditions of containment of a circle in an ellipse, an ellipse in an ellipse, an ellipse in a region bounded by a parabola are constructed. The analytical conditions are constructed on the basis of the equations of the boundaries of the corresponding objects (areas) and then are reduced to the form of a system of inequalities depending on the placement parameters of the objects and the parameter, which is the solution of a certain equation of one variable. Based on the obtained systems of inequalities, the corresponding Φ-functions are constructed.

Keywords: ellipses, parabola, non-intersection, containment, Φ-функції-functions .

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