一类曲面族约束下的最速落径问题

Problem of the Quickest Descent Restricted by Family of One-kind Surfaces

继文献[1]之后,讨论一类可展曲面族π_λ∶y=2(λz)^(1/2) (λ,z≥0,λ是参数)约束下的落径问题。给出了依赖于参数λ的落径轨迹族 x=(λc)^(1/2)+(λ+c)sin^(-1)(c/(λ+c))^(1/2)-((λ+z)(c-z))^(1/2)-(λ+c)sin^(-1)((c-z)/(λ+c))^(1/2) y^2=4λz (λ≥0)及包络面方程。最后讨论了降落时间与参数λ的关系.

In this paper, the problem of the most fast drop in level restricted by a family of one-kind expansible surface πλ:y =2λz(λ,z≥0, λ is parameter) was discussed. The family of locus of drop in level which is dependent on parameter λ and the equation of the wrapped surface are given. The relationship between the falling time and the parameter X was also discussed.