## Advanced Mathematics and Mechanics Applications Using by David Halpern, Howard B. Wilson, Louis H. Turcotte

By David Halpern, Howard B. Wilson, Louis H. Turcotte

Due to the fact that its creation in 1984, MATLAB's ever-growing recognition and performance have secured its place as an industry-standard software program package deal. The ordinary, interactive surroundings of MATLAB 6.x, which incorporates a high-level programming language, flexible pics services, and abundance of intrinsic features, is helping clients concentrate on their functions instead of on programming mistakes. MATLAB has now leapt some distance sooner than FORTRAN because the software program of selection for engineering functions.

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**Extra resources for Advanced Mathematics and Mechanics Applications Using MATLAB, Third Edition**

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Range - a vector used by function axis to set % window limits to plot x,y,z points % undistorted. This vector has the form % [xmin,xmax,ymin,ymax] when xyz has % only two columns or the form % [xmin,xmax,ymin,ymax,zmin,zmax] % when xyz has three columns. 5 Nonlinear Motion of a Damped Pendulum Motion of a simple pendulum is one of the most familiar dynamics examples studied in physics. The governing equation of motion can be satisfactorily linearized for small oscillations about the vertical equilibrium position, whereas nonlinear effects become important for large deßections.

To satisfy the end conditions, F (x) must be an odd-valued function of period 2l. Introducing a function g(x) such that g(x) = f (x), 0 ≤ x ≤ l and g(x) = −f (2l − x), l < x ≤ 2l leads to F (x) = sign(x)g(rem(abs(x), 2l)) where the desired periodicity is achieved using the MATLAB remainder function, rem. This same problem can also be solved using a Fourier sine series (see chapter 9). For the present we concentrate on the solution just obtained. A program was written to implement the translating wave solution when f (x) is a piecewise linear function computed using interp1.

The differential equation for the problem is deÞned as function zdot on lines 26 and 27. 4: Angular Deßection versus Time for Pendulum Pushed Over the Top by calls to function ode45 on lines 59, 75, and 80. Integration tolerance values were chosen at line 30, and a time span for the simulation is deÞned interactively at lines 46 and 47. Function penanim(t,th,titl,tim) plots theta versus time and animates the system response by computing the range of (x,y) values, Þxing the window size to prevent distortion, and sequentially plotting positions of the pendulum to show the motion history.