6533b856fe1ef96bd12b2887
RESEARCH PRODUCT
The tennis racket effect in a three-dimensional rigid body
Pavao MardešićDominique SugnyDominique SugnyLéo Van Dammesubject
[ MATH ] Mathematics [math]media_common.quotation_subject[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]Euler anglesFOS: Physical sciencesPhysics - Classical PhysicsInertiaRotation01 natural sciences010305 fluids & plasmassymbols.namesakeSimple (abstract algebra)0103 physical sciencesRacketClassical mechanics[MATH]Mathematics [math]010306 general physicsmedia_commonMathematicscomputer.programming_language[PHYS]Physics [physics][ PHYS ] Physics [physics]Dynamics (mechanics)Classical Physics (physics.class-ph)Statistical and Nonlinear PhysicsMoment of inertiaCondensed Matter PhysicsRigid bodyEuler anglesClassical mechanicsGeometric effectsymbols[ PHYS.MPHY ] Physics [physics]/Mathematical Physics [math-ph]computerdescription
We propose a complete theoretical description of the tennis racket effect, which occurs in the free rotation of a three-dimensional rigid body. This effect is characterized by a flip ($\pi$- rotation) of the head of the racket when a full ($2\pi$) rotation around the unstable inertia axis is considered. We describe the asymptotics of the phenomenon and conclude about the robustness of this effect with respect to the values of the moments of inertia and the initial conditions of the dynamics. This shows the generality of this geometric property which can be found in a variety of rigid bodies. A simple analytical formula is derived to estimate the twisting effect in the general case. Different examples are discussed.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-01-01 | Physica D: Nonlinear Phenomena |