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Past exam of the mathematics course of the University of Cambridge
/
2024
/
iii
/
Paper 329
/
2
/
c
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Mathematics course of the University of Cambridge
Past exam of the mathematics course of the University of Cambridge
2024
iii
Paper 329
2
2026-09-28
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Solution
c
Solution
0
0
0
c
For pure
translation
, integrate the
slender-body force density
over each rod and take its
moment
about
O
. The three coordinate directions give
U
U
e
x
U
e
y
U
e
z
F
/
(
C
LU
)
(
5
,
0
,
0
)
(
0
,
5
,
0
)
(
0
,
0
,
5
)
G
/
(
C
L
2
U
)
(
0
,
1
,
0
)
(
1
,
0
,
0
)
(
0
,
0
,
0
)
.
(1)
Thus
F
=
5
C
L
U
,
G
=
C
L
2
(
U
y
,
U
x
,
0
)
(2)
when
Ω
=
0
.
Let
K
=
0
1
0
1
0
0
0
0
0
,
D
=
13/3
0
0
0
13/3
0
0
0
4/3
.
(3)
The
symmetry
proved in part (
a
) determines
the force
generated by
rotation
from the
translation
-generated couple. Combining this with the given rotational resistance gives the complete
matrix
(
F
G
)
=
C
(
5
L
I
L
2
K
L
2
K
L
3
D
)
(
U
Ω
)
.
(4)
Ancestors
(10)
2
Paper 329
iii
2024
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
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