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

Considering that its advent in 1984, MATLAB's ever-growing acceptance and performance have secured its place as an industry-standard software program package deal. The simple, interactive setting of MATLAB 6.x, which incorporates a high-level programming language, flexible pics services, and abundance of intrinsic services, is helping clients specialize in their purposes instead of on programming blunders. MATLAB has now leapt a ways sooner than FORTRAN because the software program of selection for engineering functions.

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That idea was not explored. To assess the accuracy of the spline interpolation, values for ˆ −B ˆ approx ) and |(k − kapprox )/k| were obtained at 101 sample points along norm(B the curve. 15 show errors in the third decimal place except near the ends of the interpolation interval where a “not a knot” boundary condition is employed [27]. 15: Error Plot © 2003 by CRC Press LLC 100 120 Program Output and Code Program splinerr 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: function splinerr % Example: splinerr % ~~~~~~~~~~~~~~~~~ % % This program calculates the binormal and % curvature error for a spiral space curve.

The block % slides on a horizontal plane which provides % viscous damping. 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24: % % % % % % % % % % example - Omit this parameter for interactive input. Use smdplot(1) to run a sample problem. t,X - time vector and displacement response m,c,k - mass, damping coefficient, spring stiffness constant f1,f2,w - force components and forcing frequency x0,v0 - initial position and velocity User m functions called: spring smdsolve inputv ----------------------------------------------- 25: 26: 27: 28: 29: 30: 31: pltsave=0; disp(’ ’), disp(...

The torsion is only encountered when the time derivative of acceleration is considered. This is seldom of interest in Newtonian mechanics. ˆ B, ˆ κ, and τ in terms of R (t), A function crvprp3d was written to evaluate Tˆ , N, R (t), and R (t). Another function aspiral applies crvprp3d to the curve described by R(t) = [(ro + kt) cos(t); (ro + kt) sin(t); ht] where t is the polar coordinate angle for cylindrical coordinates. 14 depicts results generated from the default data set where ro = 2π , k = 1 , h = 2 , 2π ≤ t ≤ 8π, with 101 data points being used.

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

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