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This chapter describes the numerical and symbolic solution of systems of ordinary differential equations (ODEs). In numerical solutions it is necessary to control the errors, a topic that will be covered with examples using the popular numerical MATLAB solver ode45. For symbolic solutions we will use the MATLAB dsolve function. We will also show how to use symbolic algebra to define the function needed by ode45 to obtain a numerical solution. The ODEs that govern engineering dynamics problems are often best described through animation and movie functions. A particular example, the spring-pendulum, will be thoroughly solved and animated to illustrate the types of unexpected motions and behavior that can occur in even simple dynamic systems.

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Ordinary Differential Equations

  • 章节

  • 发表日期：

    2025年

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  • Lester W. Schmerr, Jr.

摘要

This chapter describes the numerical and symbolic solution of systems of ordinary differential equations (ODEs). In numerical solutions it is necessary to control the errors, a topic that will be covered with examples using the popular numerical MATLAB solver ode45. For symbolic solutions we will use the MATLAB dsolve function. We will also show how to use symbolic algebra to define the function needed by ode45 to obtain a numerical solution. The ODEs that govern engineering dynamics problems are often best described through animation and movie functions. A particular example, the spring-pendulum, will be thoroughly solved and animated to illustrate the types of unexpected motions and behavior that can occur in even simple dynamic systems.