blending curves for landing problems by numerical differential equations

• Main Authors: Huang, Hung Tsai, 黃宏財
• Other Authors: Li, Zi Cai
• Format: Others
• Language: en_US
• Published: 1996
• Online Access: http://ndltd.ncl.edu.tw/handle/08947173701712567502

碩士 === 國立中山大學 === 應用數學研究所 === 84 === The paper presents new numerical techniques to blend 3-D curves satisfying some containment and tangent requirements. Their parametric functions x(s),y(s) and z(s) are governed by the fourth order ordinary differential equations (ODEs). New techniques are proposed to deal with arbitrariness arising from the tangent requirements in the parametric functions. The Hermite finite element methods are adopted to solve a system of boundary value problems of the fourth order ODEs, accompanied with a brief error analysis. The important results in this thesis lie in exploration on the conditions of unique solutions and the consistent conditions of infinite solutions to both ODE and FEM. Numerical experiments have been carried out to confirm the error analysis made, and constructed some good blending curves. The results have applied directly to the airplane landing where the landing point is arbitrary along the airstrip, and other kinds of trajectory problems. The study of this paper can also be applied to blending curves and surfaces of airlpane, ships, grand building and astronautic shuttle- station.