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