# gst: dynamics of perturbed elliptical billiard tables.

<< ️Dynamical billiards consist of a particle on a two-dimensional table, bouncing elastically off a boundary curve. The state of the system is given by two numbers: one describing the location along the curve where the bounce occurs, and another describing the incoming angle of the bounce. Successive bounces define a two-dimensional area preserving map, and iterating this map gives a dynamical system first studied by Birkhoff. >>

<< ️One of the simplest smooth table shapes is that of an ellipse, in which case the dynamics of the billiard map is completely integrable. The longstanding Birkhoff conjecture is that elliptical tables are the only smooth convex table for which complete integrability occurs. >>

<< ️In this spirit, (AA) present an implicit real analytic method for iterating billiard maps on perturbed elliptical tables. This method allows (They) to compute local stable and unstable manifolds of periodic orbits using the parameterization method. Globalizing these local manifolds numerically provides insight into the dynamics of the table. >>

Patrick Bishop, Summer Chenoweth, Emmanuel Fleurantin, et al. Dynamics of perturbed elliptical billiard tables. arXiv: 2602.15272v1 [math.DS]. Feb 17, 2026.

https://arxiv.org/abs/2602.15272

Also: billiard, particle, bouncing, elastic, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, billiard, particles, bouncing, elasticity, perturbed elliptical table.

# gst: apropos of odd droplets; fluids with broken symmetries could self-control their mechanics.

<< Flows with deformable interfaces are commonly controlled by applying an external field or modifying the boundaries that interact with the fluid, (..) Here, (AA) demonstrate that fluids with broken symmetries can self-control their mechanics. (They) demonstrate that odd viscosity dramatically disrupts conventional symmetric spreading by inducing asymmetric deformations and chiral flow patterns. (Their) analysis reveals a variety of dynamic regimes, including leftward and rightward bouncing, as well as rolling, depending on the relative strength of the odd viscosity. >>️

Hugo França, Maziyar Jalaal. Odd Droplets: Fluids with Odd Viscosity and Highly Deformable Interfaces. arXiv: 2503.21649v1 [cond-mat.soft]. Mar 27, 2025.

https://arxiv.org/abs/2503.21649

Also: drop, droplet, droploid, chiral, bouncing, rolling, slipping, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, drop, droplet, droploid, chirality, bouncing, rolling, slipping, oddity, odd viscosity, self-control

# gst: apropos of synchronization of large bubble clouds, self-oscillating acoustic bubbles that bounce

<< Self-oscillations underlie many natural phenomena such as heartbeat, ocean waves, and the pulsation of variable stars. (..) In this study, (AA) consider two closely spaced bubbles pulsating in the kHz range in response to ultrasonic excitation. A translational bouncing motion emerges from their interaction with a much lower frequency than the bubble pulsation frequency. >>

Their analysis << reveals that the observed bubble bouncing exhibits the main features of self-oscillation, such as negative damping and the emergence of a limit cycle. These results highlight unexpected nonlinear effects in the field of microbubbles and give insights into the understanding of synchronization in large bubble clouds. >>️

Gabriel Regnault, Alexander A Doinikov, et al. Phenomenon of self-oscillation in bubble dynamics: Bouncing acoustic bubbles. arXiv: 2404.05822v1 [physics.flu-dyn]. Apr 8, 2024.

https://arxiv.org/abs/2404.05822

Also: bubble, bouncing, behav, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, bubble, self-oscillation, bouncing, behavior, collective behavior, bouncing motion, synchronization

# gst: apropos of bouncing, even balls that undergo rolling are typically found to lift off slipping.

<< A detailed set of experiments are described that capture over a 1000 different instances of the bounce of a golf ball. (..) Data are presented from two different turfs; one artificial and one from a typical tee. >>

<< A better fit to the data is found using a non-physical piecewise-affine landing to lift-off relationship, which distinguishes between cases that bounce in pure slip from those that undergo rolling. Nevertheless, even balls that undergo rolling are typically found to lift off slipping, having undergone spin reversal. >>

Stanisław W. Biber, Kristian M. Jones, et al. Measurements and linearized models for golf ball bounce. arXiv: 2302.02758v1 [physics.class-ph]. Jan 13, 2023. 

https://arxiv.org/abs/2302.02758

Also

keyword 'bouncing' | 'rolling' | 'slipping' in FonT

https://flashontrack.blogspot.com/search?q=bouncing

https://flashontrack.blogspot.com/search?q=rolling

https://flashontrack.blogspot.com/search?q=slipping

Keywords: gst, bouncing, rolling,  slipping