Journals
Publish with us
Publishing partnerships
About us
Blog
International Scholarly Research Notices
Table of Contents
International Scholarly Research Notices
/
2012
/
Article
/
Tab 1
/
Research Article
Rigid Body Trajectories in Different 6D Spaces
Table 1
Velocity functions for the various groups.
ℝ
3
⋉
𝑆
𝑂
(
3
)
𝑆
𝑂
(
4
)
𝑆
𝐸
(
3
)
𝑆
𝑂
(
1
,
3
)
𝑣
1
(
𝑡
)
𝑣
𝑥
𝑣
𝑥
𝑣
𝑥
𝑣
𝑥
𝑣
2
(
𝑡
)
𝑣
𝑦
c
o
s
(
𝑓
)
𝑣
𝑦
c
o
s
(
𝑤
4
𝑡
+
𝑓
)
𝑣
𝑦
c
o
s
(
𝑤
5
𝑡
+
𝑓
)
𝑣
𝑦
c
o
s
(
𝑤
6
𝑡
+
𝑓
)
𝑣
3
(
𝑡
)
𝑣
𝑦
s
i
n
(
𝑓
)
𝑣
𝑦
s
i
n
(
𝑤
4
𝑡
+
𝑓
)
𝑣
𝑦
s
i
n
(
𝑤
5
𝑡
+
𝑓
)
𝑣
𝑦
s
i
n
(
𝑤
6
𝑡
+
𝑓
)
𝑤
1
(
𝑡
)
𝑤
𝑤
𝑤
𝑤
𝑤
2
(
𝑡
)
0
0
0
0
𝑤
3
(
𝑡
)
0
0
0
0
𝑤
4
=
(
1
−
𝑜
1
/
𝑚
)
𝑤
𝑤
5
=
𝑤
𝑤
6
=
(
1
+
𝑜
1
/
𝑚
)
𝑤