Dynamics of Golf Ball-Hole Interactions: Rolling Around the Rim

1999 ◽  
Vol 121 (1) ◽  
pp. 88-95 ◽  
Author(s):  
Mont Hubbard ◽  
Tait Smith
Keyword(s):  
Initial Conditions ◽  
Golf Ball ◽  
Capture Process ◽  
Velocity Impact ◽  
Ball Rolling ◽  
Pure Rolling ◽  
Rolling Without Slipping ◽  
Impact Parameter Space ◽  
Roll Out ◽  
Perturbation Solutions

A previous study of a golf ball rolling on the rim of a cup neglected the spin of the ball about a line perpendicular to the plane of contact. The capture process is studied here by numerically solving the equations for rolling without slipping on the rim. The boundary in the velocity-impact parameter space separating roll-in and roll-out trajectories corresponds to initial conditions for a set of near guasi-equilibrium trajectories. Stability of the equilibrium trajectories is investigated using symbolic linearization of perturbation solutions from them. Although the locally unstable equilibrium trajectories themselves are not attainable from the two-space of pure rolling initial conditions, the boundary is nevertheless a “barrier” in that it corresponds to long contact times and large roll around angles.

Numerical Study of Superharmonic Resonances in a Mistuned Horizontal-Axis Wind-Turbine Blade-Rotor Set

2019 ◽  
Author(s):  
Ayse Sapmaz ◽  
Gizem D. Acar ◽  
Brian F. Feeny
Keyword(s):  
Wind Turbine ◽  
Initial Conditions ◽  
Numerical Study ◽  
Horizontal Axis ◽  
Rotor Speed ◽  
Horizontal Axis Wind Turbine ◽  
First Order ◽  
Direct Excitation ◽  
Rotor Angle ◽  
Perturbation Solutions

Abstract This paper is on a simplified model of an in-plane blade-hub dynamics of a horizontal-axis wind turbine with a mistuned blade. The model has cyclic parametric and direct excitation due to gravity and aerodynamics. This work follows up a previous perturbation study applied to the blade equations written in the rotor-angle domain and decoupled from the hub, in which superharmonic and primary resonances were analyzed. In this work, the effects of mistuning, damping, and forcing level are illustrated. The first-order perturbation solutions are verified with comparisons to numerical simulations at superharmonic resonance of order two. Additionally, the effect of rotor loading on the rotor speed and blade amplitudes is investigated for different initial conditions and mistuning cases.

scholarly journals Rolling of a rigid ball on a horizontal deformable surface

2004 ◽  
Vol 46 (2) ◽  
pp. 249-264
Author(s):  
Maurice N. Brearley ◽  
Neville J. De Mestre
Keyword(s):  
Finite Strain ◽  
Strain Theory ◽  
Golf Ball ◽  
Rigid Sphere ◽  
Billiard Ball ◽  
Ball Rolling ◽  
Deformable Surface ◽  
Finite Strain Theory ◽  
Theoretical Results

AbstractThe rolling of a ball on a horizontal deformable surface was investigated under the assumptions that the ball was a rigid sphere and the surface was elastic. Finite strain theory was used to develop theoretical results which were found to match observations well in cases where the ball and surface involved were such as to ensure no slipping at the region of contact, including a lawn bowl rolling on a grass rink and a billiard ball rolling on carpet. The theory did not match well the behaviour of a golf ball on a grass green because the ball was too light to enforce the no-slipping condition.

scholarly journals Formation of exoplanetary satellites by pull-down capture

2019 ◽  
Vol 5 (10) ◽  
pp. eaaw8665 ◽  
Author(s):  
Bradley M. S. Hansen
Keyword(s):  
Initial Conditions ◽  
Giant Planet ◽  
Giant Planets ◽  
Capture Process ◽  
Satellite Formation ◽  
Large Size ◽  
Numerical Integrations ◽  
The Stability ◽  
Gaseous Envelope ◽  
Original Configuration

The large size and wide orbit of the recently announced exomoon candidate Kepler-1625b-i are hard to explain within traditional theories of satellite formation. We show that these properties can be reproduced if the satellite began as a circumstellar co-orbital body with the original core of the giant planet Kepler-1625b. This body was then drawn down into a circumplanetary orbit during the rapid accretion of the giant planet gaseous envelope, a process termed “pull-down capture.” Our numerical integrations demonstrate the stability of the original configuration and the capture process. In this model, the exomoon Kepler-1625b-i is the protocore of a giant planet that never accreted a substantial gas envelope. Different initial conditions can give rise to capture into other co-orbital configurations, motivating the search for Trojan-like companions to this and other giant planets.

Kinematics Analysis and Simulation of Small Satellite Docking Mechanism End Executor

2014 ◽  
Vol 487 ◽  
pp. 460-464
Author(s):  
Yuan Zhang ◽  
Ying Ying Wang ◽  
Yan Song ◽  
Li Li Zhou
Keyword(s):  
Simulation Analysis ◽  
Initial Conditions ◽  
Control Function ◽  
Space Mission ◽  
Kinematics Analysis ◽  
Capture Process ◽  
Adams Software ◽  
Docking Mechanism ◽  
New Type ◽  
And Control

In order to save space mission cost, prolonging the working life of the spacecraft and improving the flexibility and capable of performing various tasks should get more attention on orbit servicing technology. For the docking process of a new type of two independent service in-orbit spacecraft, this paper finished the kinematics analysis, for the whole docking capture process, two groups of different initial conditions and control function of the simulation analysis were finished by the ADAMS software. The results prove that the docking mechanism performance is very good, and reliable connection can be realized in the general initial conditions.

scholarly journals Perturbation Solutions to Fifth Order Over-damped Nonlinear Systems

2019 ◽  
pp. 1-11
Author(s):  
Harun-Or- Roshid ◽  
M. Zulfikar Ali ◽  
Pinakee Dey ◽  
M. Ali Akbar
Keyword(s):  
Nonlinear Systems ◽  
Initial Conditions ◽  
Approximate Solutions ◽  
First Order ◽  
Engineering Problems ◽  
Kbm Method ◽  
Fifth Order ◽  
Physical Phenomena ◽  
Good Agreement ◽  
Perturbation Solutions

Fifth order over-damp nonlinear differential systems can be used to describe many engineering problems and physical phenomena occur in the nature. In this article, the Krylov-Bogoliubov-Mitropolskii (KBM) method has been extended to investigate the solution of a certain fifth order over-damp nonlinear systems and desired result has been found. The implementation of the presented method is illustrated by an example. The first order analytical approximate solutions obtained by the method for different initial conditions show a good agreement with those obtains by numerical method.

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