moments of inertia and the angular velocity as shown by Samarasinha and Mueller
(2015). The Euler angle, φ, is given by
φ ¼ tan
À1 I c Ω c
I b Ω b
ð2:48Þ
and its first derivative is
_
φ ¼ ÀΩ a
I a À I c
ð
ÞI c Ω
2
c þ I a À I b
ð
ÞI b Ω
2
b
I
2
c Ω
2
c þ I
2
b Ω
2
b
!
ð2:49Þ
The other first derivatives are
_
ϕ ¼ L
I c Ω
2
c þ I b Ω
2
b
I
2
c Ω
2
c þ I
2
b Ω
2
b
!
ð2:50Þ
and
_
θ ¼ Ω c cos φ À Ω b sin φ
ð2:51Þ
Fig. 2.11 Euler angle definitions (Following Landau and Lifshitz (1976); Copyright Elsevier 1976.
Used with permission)
50
2 The Nucleus
(2015). The Euler angle, φ, is given by
φ ¼ tan
À1 I c Ω c
I b Ω b
ð2:48Þ
and its first derivative is
_
φ ¼ ÀΩ a
I a À I c
ð
ÞI c Ω
2
c þ I a À I b
ð
ÞI b Ω
2
b
I
2
c Ω
2
c þ I
2
b Ω
2
b
!
ð2:49Þ
The other first derivatives are
_
ϕ ¼ L
I c Ω
2
c þ I b Ω
2
b
I
2
c Ω
2
c þ I
2
b Ω
2
b
!
ð2:50Þ
and
_
θ ¼ Ω c cos φ À Ω b sin φ
ð2:51Þ
Fig. 2.11 Euler angle definitions (Following Landau and Lifshitz (1976); Copyright Elsevier 1976.
Used with permission)
50
2 The Nucleus