# Download Computer Algebra Recipes for Classical Mechanics by Richard H. Enns, George C. McGuire (auth.) PDF

By Richard H. Enns, George C. McGuire (auth.)

ISBN-10: 0817642919

ISBN-13: 9780817642914

ISBN-10: 146120013X

ISBN-13: 9781461200130

Hundreds of novel and leading edge laptop algebra "recipes" will allow readers beginning on the moment 12 months undergraduate point to simply and quickly remedy and discover such a lot difficulties they come across of their classical mechanics experiences. utilizing the strong desktop algebra approach MAPLE (Release eight) - no earlier wisdom of MAPLE is presumed - the proper command buildings are defined on a need-to-know foundation because the recipes are built. This new problem-solving consultant can serve within the lecture room or for self-study, for reference, or as a textual content for an online course.

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Extra info for Computer Algebra Recipes for Classical Mechanics

Example text

For i = 1,2, ... , the entry til i generates t1 = TIN, t2 = 2 TIN, etc. > til i:=i*T/N; The position f of the train is evaluated at time til i, the components being placed in a list and assigned the name pt I I i. The point pt I I i is then plotted in PL II i as a size 14 blue circle with pointplot, and the do loop ended. 3 SUPPLEMENTARY RECIPES 45 The circular portion of track of radius R is plotted in PP with the polarplot command and colored brown. Mike adds appropriate labels in TP to the three vectors with the textplot command.

The boat is able to maintain a fixed angular heading and a speed which is n times the river's average speed. The boat leaves the south bank at the point (x = 0, y = -w/2) and intends to land on the north bank at (0, w/2). The questions to be answered are as follows: (a) What does the velocity profile of the river look like? (b) What are the maximum and average speeds of the river? ( c) How does the angular heading depend on n? (d) How does the time it takes the boat to cross the river depend on n?

Y:=int(v[2] ,tt=O .. t)-w/2; y := n (153 arctan(5) - ~) sin (B) t - 500 Setting y = 0 and solving for t yields the time thalf it takes to cross half-way across the river. - n sin( B) (26 arctan(5) - 5) The symmetry of the river's velocity profile implies that x = 0 at t = thalf. Thus, we integrate the first component of the velocity v over the time interval t = O.. thalf, set the result equal to zero, and simplify the lengthy output (not shown here) with the radical simplification (radsimp) command.