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Applied Calculus of Variations for Engineers, 2nd Edition
book

Applied Calculus of Variations for Engineers, 2nd Edition

by Louis Komzsik
June 2014
Intermediate to advanced content levelIntermediate to advanced
233 pages
5h 42m
English
CRC Press
Content preview from Applied Calculus of Variations for Engineers, 2nd Edition
18 Applied calculus of variations for engineers
reach the terminal point of the curve at the same time. This is also counter-
intuitive, since clearly they have different geometric distances to cover; how-
ever, since they are acting under the gravity and the slope of the curve is
different at the two locations, the particle starting from a higher location
gathers much bigger speed than the particle starting at a lower location.
This so-called tautochrone behavior may be proven by calculation of the
time of the particles using the formula developed earlier. Evaluation of this
integral between points (x
0
,y
0
)and(x
1
,y
1
) as well as between (x
2
,y
2
)and
(x
1
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Publisher Resources

ISBN: 9781482253597