The tennis racket effect in a three-dimensional rigid body
- Resource Type
- Authors
- Pavao Mardešić; Dominique Sugny; Léo Van Damme
- Source
- Physica D: Nonlinear Phenomena
Physica D: Nonlinear Phenomena, 2017, 338, pp.17-25. ⟨10.1016/j.physd.2016.07.010⟩
Physica D: Nonlinear Phenomena, Elsevier, 2017, 338, pp.17-25. 〈10.1016/j.physd.2016.07.010〉
Physica D: Nonlinear Phenomena, Elsevier, 2017, 338, pp.17-25. ⟨10.1016/j.physd.2016.07.010⟩
- Subject
- [ MATH ] Mathematics [math]
media_common.quotation_subject
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]
Euler angles
FOS: Physical sciences
Physics - Classical Physics
Inertia
Rotation
01 natural sciences
010305 fluids & plasmas
symbols.namesake
Simple (abstract algebra)
0103 physical sciences
Racket
Classical mechanics
[MATH]Mathematics [math]
010306 general physics
media_common
Mathematics
computer.programming_language
[PHYS]Physics [physics]
[ PHYS ] Physics [physics]
Dynamics (mechanics)
Classical Physics (physics.class-ph)
Statistical and Nonlinear Physics
Moment of inertia
Condensed Matter Physics
Rigid body
Geometric effect
symbols
[ PHYS.MPHY ] Physics [physics]/Mathematical Physics [math-ph]
computer
- Language
- ISSN
- 0167-2789
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.
Comment: 20 pages, 11 figures, submitted to Physica D (2016)