一种不规范的斯特姆-刘维本征值问题  

One question on the irregular Sturm-Liouville eigenvalue problem

作　　者：程利青[1] 

机构地区：[1]福州大学电子科学与应用物理系,福建福州350002

出　　处：《大学物理》2003年第2期11-14,共4页College Physics

摘　　要：由于端点系有集中质量的弹性杆的振动问题的边界条件不是斯特姆 -刘维本征值问题所要求的边界条件 ,分离变数所得到的函数系 {Xn(x) }不是正交函数系 ,故求解十分困难 .本文提出一种变换 ,将其边界条件化为第一类、第二类或第三类边界条件 ,此时 {Xn(x) }为正交完备函数系 ,问题大为简化 .It's very difficult to solve the oscillation problem of elastic rod with concentrated mass on the end because the boundary condition in this case is not the one required by Sturm Liouville eigenvalue problem and the functions{X n(x)} are not orthogonal ones.This problem is simplified by presenting a transformation,with which the boundary condition is changed to the boundary condition of first ,second or third class and then the functions {X n(x)}are orthogonal complete functions.Some solutions to such problems with different ends are discussed .

关 键 词：斯特姆-刘维本征值问题 边界条件 本征函数 固有频率 不规范性 振动 弹性杆 

分 类 号：O326[理学—一般力学与力学基础] O411.1[理学—力学]