Astronomical Applications Department, U.S. Naval Observatory Curves 3 D Page 5
>
kappa=kappa( Helix( Lissajous(n,m,a,b,phi,t), c, t), t );
c
2 b2 (
)
sin
+
m t
2 m4 c2 a2 ( )
sin
n t
2 n4
+
=
(
)
-
+
a
(
)
cos
n t n b
(
)
sin
+
m t
m
2
b
(
)
cos
+
m t
m a
(
)
sin
n t n
2
2
+
/
1 2
(
)
+
+
a
2
(
)
cos
n t
2 n2 b2
(
)
cos
+
m t
2 m2 c2
/
3 2
>
tau=tau( Helix( Lissajous(n,m,a,b,phi,t), c, t), t );
-
+
c b
(
)
sin
+
m t
m
2 a
(
)
cos
n t n
3
c a
(
)
sin
n t n
2 b
(
)
cos
+
m t
m
3
(
)
=
c
2 b2 (
)
sin
+
m t
2 m4 c2 a2 ( )
sin
n t
2 n4
+
(
)
-
+
a
(
)
cos
n t n b
(
)
sin
+
m t
m
2
b
(
)
cos
+
m t
m a
(
)
sin
n t n
2
2
+
Junk
>
tau=tau( Twicubic(t), t );
Page 5
