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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
130 Applied calculus of variations for engineers
the derivative for k =2as
d
dt
B
i,2
(t)=B
i,2
(t)=
2
t
i+2
t
i
B
i,1
2
t
i+3
t
i+1
B
i+1,1
.
By induction, for any k value the first derivative is as follows:
d
dt
B
i,k
(t)=B
i,k
(t)=
k
t
i+k
t
i
B
i,k1
(t)
k
t
i+k+1
t
i+1
B
i+1,k1
(t).
A repeated application of the same step will produce the needed second deriva-
tive B

as
d
dt
B
i,k
(t)=B

i,k
(t)=
k
t
i+k
t
i
B
i,k1
(t)
k
t
i+k+1
t
i+1
B
i+1,k1
(t).
The spline, besides being smooth (minimal in curvature), is expected to ap-
proximate a given set of points P
j
; j =0,...,m,with associated prescribed pa-
rameter values (not necessarily identical to the knot values) of t
j
; j =0,...,m.
If suc ...
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Publisher Resources

ISBN: 9781482253597