August 2013
Intermediate to advanced
608 pages
21h 36m
English
Content preview from Ballistics, 2nd Edition
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273Trajectories
By dening a specic angular momentum, h = H/I
T
, we can write
hii
i
=+×
Ip
It
P
T
d
d
(8.226)
If we take the derivative of Equation 8.226 with respect to time, we get
d
d
d
d
d
d
d
d
d
d
P
T
P
T
2
h
i
iii
i
i
t
I
I
p
Ip
It tt t
=+ +×
+×
2
(8.227)
Since the cross-product of a vector with itself is zero, we get
d
d
d
d
d
d
P
T
P
T
2
h
i
i
i
i
t
I
I
p
Ip
It t
=+ +×
2
(8.228)
In anticipation of a later need, we shall take the dot product and cross-product of the vector h
with the unit vector i to get
hi ii
i
i⋅= +×
⋅=
Ip
It
Ip
I
P
T
P
T
d
d
(8.229)
hi ii
i
i
i
×= +×
×=
Ip
It
t
P
T
d
d
d
d
(8.230)
In Equations 8.229 and 8.230, we have used the orthogonality properties of ...
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