The tennis racket theorem is a result in classical mechanics describing movement of a rigid body with three distinct principal moments of inertia. It is also dubbed the Dzhanibekov effect, after Russian astronaut Vladimir Dzhanibekov who discovered the theorem’s consequences while in space in 1985.
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Clear["Global`*"]
Equations:
I
x
*
ω
x
'[t]+(
I
y
-
I
z
)*
ω
y
[t]*
ω
z
[t]0,​​
I
y
*
ω
y
'[t]+(
I
z
-
I
x
)*
ω
x
[t]*
ω
z
[t]0,​​
I
z
*
ω
z
'[t]+(
I
x
-
I
y
)*
ω
x
[t]*
ω
y
[t]0,​​​​
ω
x
[t]=Sin[ψ[t]]Sin[ϑ[t]]ϕ'[t]+Cos[ψ[t]]ϑ'[t],​​
ω
y
[t]=Cos[ψ[t]]Sin[ϑ[t]]ϕ'[t]-Sin[ψ[t]]ϑ'[t],​​
ω
z
[t]=Cos[ϑ[t]]ϕ'[t]+ψ'[t]
In[]:=
TIME=50;​​
I
x
=1;​​
I
y
=2;​​
I
z
=30;​​{Xx,Yy,Zz}=NDSolveValue​​
I
x
*(Cos[ϑ[t]]Sin[ψ[t]]
′
ϑ
[t]
′
ϕ
[t]-Sin[ψ[t]]
′
ϑ
[t]
′
ψ
[t]+Cos[ψ[t]]Sin[ϑ[t]]
′
ϕ
[t]
′
ψ
[t]+Cos[ψ[t]]
′′
ϑ
[t]+Sin[ϑ[t]]Sin[ψ[t]]
′′
ϕ
[t])+(
I
y
-
I
z
)*(Cos[ψ[t]]Sin[ϑ[t]]ϕ'[t]-Sin[ψ[t]]ϑ'[t])*(Cos[ϑ[t]]ϕ'[t]+ψ'[t])0,​​
I
y
*(Cos[ϑ[t]]Cos[ψ[t]]
′
ϑ
[t]
′
ϕ
[t]-Cos[ψ[t]]
′
ϑ
[t]
′
ψ
[t]-Sin[ϑ[t]]Sin[ψ[t]]
′
ϕ
[t]
′
ψ
[t]-Sin[ψ[t]]
′′
ϑ
[t]+Cos[ψ[t]]Sin[ϑ[t]]
′′
ϕ
[t])+(
I
z
-
I
x
)*(Sin[ψ[t]]Sin[ϑ[t]]ϕ'[t]+Cos[ψ[t]]ϑ'[t])*(Cos[ϑ[t]]ϕ'[t]+ψ'[t])0,​​
I
z
*(-Sin[ϑ[t]]
′
ϑ
[t]
′
ϕ
[t]+Cos[ϑ[t]]
′′
ϕ
[t]+
′′
ψ
[t])+(
I
x
-
I
y
)*(Sin[ψ[t]]Sin[ϑ[t]]ϕ'[t]+Cos[ψ[t]]ϑ'[t])*(Cos[ψ[t]]Sin[ϑ[t]]ϕ'[t]-Sin[ψ[t]]ϑ'[t])==0,​​ψ[0]0,​​ϕ[0]0,​​ϑ[0]π2,​​ϕ'[0]-π2,​​ψ'[0]0.00001,​​ϑ'[0]0.00001,​​{ϕ,ψ,ϑ},{t,0,TIME};​​
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time

References

◼
  • [1]: http://en.wikipedia.org/wiki/Tennis_racket_theorem
    • ◼
  • [2]: https://www.youtube.com/watch?v=LR5hkgfRPno
    • ◼
  • [3]: https://youtu.be/L2o9eBl_Gzw?si=jUHcIpLc9hiG8dCE
    • ◼
  • [4]: https://youtu.be/L8B83DUKiiA?si=GjMZ9TSmadQnxNKo

    • CITE THIS NOTEBOOK

    Dzhanibekov effect or tennis racket theorem​
    by Mariusz Iwaniuk​
    Wolfram Community, STAFF PICKS, 2015
    ​https://community.wolfram.com/groups/-/m/t/498246