基于常微分方程的吊索曲线模型建立及求解  

Establishing and Solving of Catenary Curve Model Based on Ode Method

作　　者：潘璐璐[1] 延伟东[1] 张莹[1] 叶正麟[1] 

机构地区：[1]西北工业大学理学院,陕西西安710129

出　　处：《数学的实践与认识》2015年第5期302-307,共6页Mathematics in Practice and Theory

摘　　要：以吊索曲线模型的建立过程为例,在不同的模型假设下,分别对吊索微元进行了受力分析,建立常微分方程初值模型,并求其解析解或者数值解,分析了模型中参数变化时,对数值解的影响.模型的建立由简入难,揭示了在实际问题建立数学模型的过程中,由浅入深的思考方式.this paper takes the establishing of the catenary curve model for example, an- alyzes the force of differential element, establishes the ordinary differential equation model and work out its analytical solution or numerical solution under different model assumptions, and analyses the influence on the numerical solution when the parameters are changing. The process of modeling is from the simple to the depth, reveal the thinking way of modeling practical problems.

关 键 词：数学建模 常微分方程 吊索曲线模型 

分 类 号：U442[建筑科学—桥梁与隧道工程] O175.1[交通运输工程—道路与铁道工程]