The One-body Problem

2015 ◽  
pp. 153-165
Author(s):  
Thanu Padmanabhan
Keyword(s):  
Body Problem ◽  
The One

GLOBAL BEHAVIOR OF THE CHARGED ISOSCELES THREE-BODY PROBLEM

1994 ◽  
Vol 04 (04) ◽  
pp. 865-884 ◽  
Author(s):  
PAU ATELA ◽  
ROBERT I. McLACHLAN
Keyword(s):  
Bifurcation Diagram ◽  
Periodic Orbits ◽  
Body Problem ◽  
Kepler Problem ◽  
Global Bifurcation ◽  
Three Body Problem ◽  
Anisotropic Kepler Problem ◽  
The One ◽  
Three Body ◽  
Limiting Value

We study the global bifurcation diagram of the two-parameter family of ODE’s that govern the charged isosceles three-body problem. (The classic isosceles three-body problem and the anisotropic Kepler problem (two bodies) are included in the same family.) There are two major sources of periodic orbits. On the one hand the “Kepler” orbit, a stable orbit exhibiting the generic bifurcations as the multiplier crosses rational values. This orbit turns out to be the continuation of the classical circular Kepler orbit. On the other extreme we have the collision-ejection orbit which exhibits an “infinite-furcation.” Up to a limiting value of the parameter we have finitely many periodic orbits (for each fixed numerator in the rotation number), passed this value there is a sudden birth of an infinite number of them. We find that these two bifurcations are remarkably connected forming the main “skeleton” of the global bifurcation diagram. We conjecture that this type of global connection must be present in related problems such as the classic isosceles three-body problem and the anisotropic Kepler problem.

scholarly journals The Misuse and Failure of the Evolutionary Argument

Disputatio ◽  
2014 ◽  
Vol 6 (39) ◽  
pp. 199-227 ◽  
Author(s):  
Joseph Corabi
Keyword(s):  
Body Problem ◽  
William James ◽  
New Criticism ◽  
Herbert Spencer ◽  
Critical Scrutiny ◽  
Mind Body Problem ◽  
The One ◽  
The Mind ◽  
Body Theory

Abstract The evolutionary argument is an argument against epiphenomenalism, designed to show that some mind-body theory that allows for the efficacy of qualia is true. First developed by Herbert Spencer and William James, the argument has gone through numerous incarnations and it has been criticized in a number of different ways. Yet many have found the criticisms of the argument in the literature unconvincing. Bearing this in mind, I examine two primary issues: first, whether the alleged insights employed in traditional versions of the argument have been correctly and consistently applied, and second, whether the alleged insights can withstand critical scrutiny. With respect to the first issue, I conclude that the proponents of the argument have tended to grossly oversimplify the considerations involved, incorrectly supposing that the evolutionary argument is properly conceived as a non-specific argument for the disjunction of physicalism and interactionist dualism and against epiphenomenalism. With respect to the second issue, I offer a new criticism that decisively refutes all arguments along the lines of the one I present. Finally, I draw positive lessons about the use of empirical considerations in debates over the mind-body problem.

scholarly journals RADIATIVE DAMPING AND FUNCTIONAL DIFFERENTIAL EQUATIONS

2011 ◽  
Vol 26 (35) ◽  
pp. 2627-2638 ◽  
Author(s):  
SUVRAT RAJU ◽  
C. K. RAJU
Keyword(s):  
Differential Equations ◽  
Body Problem ◽  
Equations Of Motion ◽  
Functional Differential Equations ◽  
General Technique ◽  
Covariant Model ◽  
Maxwell Electrodynamics ◽  
Functional Differential ◽  
The One ◽  
Radiative Damping

We propose a general technique to solve the classical many-body problem with radiative damping. We modify the short-distance structure of Maxwell electrodynamics. This allows us to avoid runaway solutions as if we had a covariant model of extended particles. The resulting equations of motion are functional differential equations (FDEs) rather than ordinary differential equations (ODEs). Using recently developed numerical techniques for stiff, retarded FDEs, we solve these equations for the one-body central force problem with radiative damping. Our results indicate that locally the magnitude of radiation damping may be well approximated by the standard third-order expression but the global properties of our solutions are dramatically different. We comment on the two-body problem and applications to quantum field theory and quantum mechanics.

The spin-orbit interaction in the one-body problem of the point structural particle

1999 ◽  
Vol 112 (9) ◽  
pp. 1023-1032
Author(s):  
E. Entralgo ◽  
B. Cabrera ◽  
M. Y. Ballester
Keyword(s):  
Body Problem ◽  
Orbit Interaction ◽  
Spin Orbit ◽  
Spin Orbit Interaction ◽  
The One

Bruteness and Supervenience

2018 ◽  
Author(s):  
Joseph Levine
Keyword(s):  
Body Problem ◽  
The Other ◽  
Robust Realism ◽  
Mind Body Problem ◽  
The One ◽  
The Mind ◽  
The Way

This chapter first presents a framework, one that the author has defended elsewhere (Levine 2001), for understanding the notion of bruteness, its relation to modality, and the way this framework applies to the mind–body problem. Second, the chapter then turns to a problem in meta-ethics and attempts to address this problem within the framework already established. The problem is how to reconcile two views that many philosophers, including the author, are inclined to hold: on the one hand, “robust realism” or “non-naturalism” about the ethical and, on the other, the supervenience of the ethical on the non-ethical. The chapter speculates about how one might reasonably reconcile these two views.

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