Dynamics and Vibrations. MATLAB tutorial

School of Engineering Brown University, 2011. — 49 pages. This tutorial is intended to provide a crash-course on using a small subset of the features of MATLAB. If you complete the whole of this tutorial, you will be able to use MATLAB to integrate equations of motion for dynamical systems, plot the results, and use MATLAB optimizers and solvers to make design decisions. You can work step-by-step through this tutorial, or if you prefer, you can brush up on topics from the list below. The tutorial contains more information than you need to start solving dynamics problems using MATLAB. If you are working through the tutorial for the first time, you should complete sections 1- 15. You can do the other sections later, when they are needed. What is MATLAB How does MATLAB differ from Mathematica? Why do we have to learn MATLAB? Starting MATLAB Basic MATLAB windows Simple calculations using MATLAB MATLAB help Errors associated with floating point arithmetic (and an example of a basic loop) Vectors in MATLAB Matrices in MATLAB Plotting and graphics in MATLAB Working with M-files MATLAB Functions Organizing complex calculations as functions in an M-file Solving ordinary differential equations (ODEs) using MATLAB Solving a basic differential equation How the ODE solver works Solving a differential equation with adjustable parameters Solving a vector valued differential equation Solving a higher order differential equation Controlling the accuracy of solutions to differential equations Looking for special events in a solution Other MATLAB differential equation solvers Using MATLAB solvers and optimizers to make design decisions Using fzero to solve equations Simple unconstrained optimization problem Optimizing with constraints Reading and writing data to/from files Movies and animation On the frustrations of scientific programming