scholarly journals New derivation of a third post-Newtonian equation of motion for relativistic compact binaries without ambiguity

2003 ◽  
Vol 68 (12) ◽  
Author(s):  
Yousuke Itoh ◽  
Toshifumi Futamase
Keyword(s):  
Equation Of Motion ◽  
Compact Binaries ◽  
Newtonian Equation

The Existence and Uniquence of the Solution for the Newtonian Equation

2010 ◽  
Vol 426-427 ◽  
pp. 334-338
Author(s):  
Yan Qing Feng ◽  
Z.H. Shen
Keyword(s):  
Periodic Solution ◽  
Basin Of Attraction ◽  
Equation Of Motion ◽  
Newtonian Equation ◽  
Coercive Function ◽  
The Basin Of Attraction

In this paper，the methods of the basin of attraction and the nonnegative coercive function are used to discuss the existence and uniquence of the periodic solution to the Newtonian equation of motion. Some Theorem is proved and the main results are generalized and discussed in this papers．

Running Speed of Goal-Seeking Rats: A Field Theoretical Analysis

1976 ◽  
Vol 43 (2) ◽  
pp. 343-349 ◽  
Author(s):  
Donald W. Griesinger
Keyword(s):  
Scalar Field ◽  
Theoretical Analysis ◽  
Potential Energy ◽  
Equation Of Motion ◽  
Running Speed ◽  
Newtonian Equation ◽  
Psychological Force ◽  
Definition Of ◽  
Maximally Smooth

Lewin introduced into psychology the concept of psychological force but was unable to specify an equation of motion, relating force to behavior. Physical analogs prove helpful in developing Lewin's ideas. The effort exerted by a hungry rat seeking food at the end of a linear runway can be defined as proportional to the gradient of a maximally smooth scalar field, whose source is the food in the goal box. This assumption leads to a direct analog between potential energy and utility in psychology. If a Newtonian equation of motion is used with this definition of force, the results compare favorably with Hull's data on rats' running behavior.

scholarly journals Applications of the Lie theory of extended groups in Hamiltonian mechanics: the oscillator and the Kepler problem

1981 ◽  
Vol 23 (2) ◽  
pp. 173-186 ◽  
Author(s):  
P. G. L. Leach
Keyword(s):  
Harmonic Oscillator ◽  
Kepler Problem ◽  
Three Dimensional ◽  
Equation Of Motion ◽  
Hamiltonian Mechanics ◽  
Lie Theory ◽  
Newtonian Equation ◽  
Constants Of Motion

AbstractThe method of the Lie theory of extended groups has recently been formulated for Hamiltonian mechanics in a manner which is consistent with the results obtained using the Newtonian equation of motion. Here the method is applied to the three-dimensional time-independent harmonic oscillator and to the classical Kepler problem. The expected constants of motion are obtained. Previously unobserved relations between generators and invariants are also noticed.

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