David Halpern, Howard B. Wilson, Louis H. Turcotte's Advanced Mathematics and Mechanics Applications Using PDF

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

ISBN-10: 158488262X

ISBN-13: 9781584882626

On the grounds that its creation in 1984, MATLAB's ever-growing attractiveness and performance have secured its place as an industry-standard software program package deal. The hassle-free, interactive atmosphere of MATLAB 6.x, which incorporates a high-level programming language, flexible photos functions, and abundance of intrinsic services, is helping clients specialise in their purposes instead of on programming mistakes. MATLAB has now leapt some distance prior to FORTRAN because the software program of selection for engineering purposes.

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7: Partial Motion Trace for Pendulum Almost Pushed Over the Top © 2003 by CRC Press LLC Program pendulum 1: 2: 3: 4: 5: 6: 7: 8: function pendulum(rundemo) % pendulum(rundemo) % This example analyzes damped oscillations of % a simple pendulum and animates the motion. 2*theta’(t)+sin(theta) = 0 9: 10: 11: 12: % Type pendulum with no argument for inter% active input. 2*theta’’(t)+sin(theta) = 0’) 23: 24: 25: 26: 27: % Create an inline function defining the % differential equation in matrix form zdot=inline(...

The initial conditions are applied to the sum of the two solution components. The particular solution is given by X(t) = real(F exp(i ω t)) with F = (f1 − if2 )/(k − m ω 2 + i c ω). The initial conditions given by this particular solution are X(0) = real(F ) and X (0) = real(i ω F ). The characteristic equation for the homogeneous equation is m s2 + c s + k = 0 which has roots s1 = (−c + r)/(2m), s2 = (−c − r)/(2m), r = c2 − 4m k. Then the homogeneous solution has the form u(t) = d(1) exp(s1 t) + d(2) exp(s2 t) where d = [1, 1; s1 , s2 ] \ [x0 − X(0); v0 − X (0)] and the complete solution is x(t) = u(t) + X(t).

42 or greater push the’) disp(... ’the pendulum over the top. ’) w0=input(’w0 = ? > ’); 41: © 2003 by CRC Press LLC if isempty(w0) | w0==0 disp(’ ’), disp(’All Done’), disp(’ ’), return end disp(’ ’) t=input([’Input a vector of time values ’,... 1:30) > ? ’]); 42: 43: 44: 45: 46: 47: 48: disp(’ ’) titl=input(’Input a title for the graphs : ’,’s’); disp(’ ’), disp(... ’Input 1 to leave images of all positions shown’) trac=input(... ’in the animation, otherwise input 0 > ? 05) close, disp(’ ’), disp(’All Done’), disp(’ ’) 84: 85: end 86: © 2003 by CRC Press LLC 87: %=============================================== 88: 89: 90: 91: 92: 93: 94: 95: 96: 97: 98: 99: 100: 101: 102: 103: 104: 105: 106: function animpen(t,th,titl,tim,trac) % % animpen(t,th,titl,tim,trac) % ~~~~~~~~~~~~~~~~~~~~~~~~~~ % This function plots theta versus t and animates % the pendulum motion % % t - time vector for the solution % th - angular deflection values defining the % pendulum positions % titl - a title shown on the graphs % tim - a time delay between successive steps of % the animation.

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


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