Prediction methods for the surf-riding threshold and the wave-blocking threshold based on Melnikov’s method

2016 ◽  
Vol 21 (2) ◽  
pp. 179-189 ◽  
Author(s):  
Atsuo Maki ◽  
Yoshiki Miyauchi
Keyword(s):  
Prediction Methods ◽  
Melnikov's Method ◽  
Melnikov’S Method ◽  
Surf Riding ◽  
Wave Blocking

A PHYSICAL INTERPRETATION OF MELNIKOV’S METHOD

1992 ◽  
Vol 02 (01) ◽  
pp. 1-9 ◽  
Author(s):  
YOHANNES KETEMA
Keyword(s):  
Physical Interpretation ◽  
Poincaré Map ◽  
Initial Conditions ◽  
Homoclinic Orbits ◽  
Poincare Map ◽  
Stable And Unstable Manifolds ◽  
Melnikov's Method ◽  
Melnikov’S Method ◽  
Sensitive Dependence ◽  
The Stability

This paper is concerned with analyzing Melnikov’s method in terms of the flow generated by a vector field in contrast to the approach based on the Poincare map and giving a physical interpretation of the method. It is shown that the direct implication of a transverse crossing between the stable and unstable manifolds to a saddle point of the Poincare map is the existence of two distinct preserved homoclinic orbits of the continuous time system. The stability of these orbits and their role in the phenomenon of sensitive dependence on initial conditions is discussed and a physical example is given.

scholarly journals Stochastic Stellar Orbits and the Shapes of Elliptical Galaxies

1987 ◽  
Vol 127 ◽  
pp. 477-478
Author(s):  
Ortwin E. Gerhard
Keyword(s):  
Elliptical Galaxies ◽  
The Other ◽  
Melnikov's Method ◽  
Stellar Orbits ◽  
Melnikov’S Method ◽  
Other Hand

Using Melnikov's method to study the appearance of stochastic orbits in perturbed Stäckel potentials, a correlation is found between the observed shapes of elliptical galaxies and the occurence of mainly regular orbits. Some other potential perturbations giving rise to large regions of stochastic orbits, on the other hand, appear to be inconsistent with observations.

A NEW AND SIMPLE CHAOS TOY

2002 ◽  
Vol 12 (08) ◽  
pp. 1843-1857 ◽  
Author(s):  
ERIK M. BOLLT ◽  
AARON KLEBANOFF
Keyword(s):  
Ball Bearing ◽  
Nonlinear Oscillations ◽  
Equations Of Motion ◽  
Future Application ◽  
Lagrangian Mechanics ◽  
Smale Horseshoe ◽  
Melnikov's Method ◽  
Melnikov’S Method ◽  
Bicycle Wheel

We present two new, and perhaps the simplest yet, mechanical chaos demonstrations. They are both designed based on a recipe of competing nonlinear oscillations. One of these devices is simple enough that using the provided description, it can be built using a bicycle wheel, a piece of wood routed with an elliptical track, and a ball bearing. We provide a thorough Lagrangian mechanics based derivation of equations of motion, and a proof of chaos based on showing the existence of an embedded Smale horseshoe using Melnikov's method. We conclude with discussion of a future application.

Spin Rotor Stabilization of a Dual-Spin Spacecraft with Time Dependent Moments of Inertia

1998 ◽  
Vol 08 (03) ◽  
pp. 609-617 ◽  
Author(s):  
V. Lanchares ◽  
M. Iñarrea ◽  
J. P. Salas
Keyword(s):  
Periodic Function ◽  
Center Of Mass ◽  
The Body ◽  
Body Motion ◽  
Time Dependent ◽  
Moments Of Inertia ◽  
Melnikov's Method ◽  
Melnikov’S Method ◽  
Principal Axes

We consider a dual-spin deformable spacecraft, in the sense that one of the moments of inertia is a periodic function of time such that the center of mass is not altered. In the absence of external torques and spin rotors, by means of the Melnikov's method we prove that the body motion is chaotic. Stabilization is obtained by means of a spinning rotor about one of the principal axes of inertia.

Analytical methods to predict the surf-riding threshold and the wave-blocking threshold in astern seas

2014 ◽  
Vol 19 (4) ◽  
pp. 415-424 ◽  
Author(s):  
Atsuo Maki ◽  
Naoya Umeda ◽  
Martin Renilson ◽  
Tetsushi Ueta
Keyword(s):  
Analytical Methods ◽  
Surf Riding ◽  
Wave Blocking
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