最小阻力功路径方程的Lei群分类及其对称性化简

Group Classification for the Path Equation Describing Minimum Drag Word and Symmetry Reductions

重新考察虑了,最早由Pakdemirli[Pakdemirli M.Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,2009,223(5):1113-1116]提出的描述最小阻力功的路径方程.将Lie群理论应用于一般方程,提出了关系任意高程函数群的分类.利用对称性,确定群不变解,并利用正则坐标,降低方程的阶次.

Path equation describing minimum drag work first proposed by Pakdemirli[Pakdemirli M.Proceedings of the Institution of Mechanical Engineers,Part C：Journal of Mechanical Engineering Science,2009,223（5）：1113-1116] was reconsidered.Lie Group theory was applied to the general equation.Group classification with respect to altitude dependent arbitrary function was presented.Using the symmetries,group-invariant solutions were determined and reduction of order by canonical coordinates was performed.