homothetic motion
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2021 ◽  
Vol 21 (2) ◽  
pp. 329-336
Author(s):  
MUTLU AKAR ◽  
SALİM YÜCE

In this study, during the 1-parameter closed homothetic motion, the Holditch-Type Theorems are presented for the polar moments of inertia of the closed orbit curves of three non-collinear points.







2015 ◽  
Vol 06 (08) ◽  
pp. 1344-1352 ◽  
Author(s):  
M. M. Wageeda ◽  
E. M. Solouma


2014 ◽  
Vol 5 (1) ◽  
pp. 305-308 ◽  
Author(s):  
Melek Masal ◽  
Soley Ersoy ◽  
Mehmet Ali Güngör


2013 ◽  
Vol 156 (2) ◽  
pp. 209-227 ◽  
Author(s):  
ADRIANA DA LUZ ◽  
EZEQUIEL MADERNA

AbstractIn this paper we study the existence and the dynamics of a very special class of motions, which satisfy a strong global minimization property. More precisely, we call a free time minimizer a curve which satisfies the least action principle between any pair of its points without the constraint of time for the variations. An example of a free time minimizer defined on an unbounded interval is a parabolic homothetic motion by a minimal central configuration. The existence of a large amount of free time minimizers can be deduced from the weak KAM theorem. In particular, for any choice ofx0, there should be at least one free time minimizerx(t)defined for allt≥ 0 and satisfyingx(0)=x0. We prove that such motions are completely parabolic. Using Marchal's theorem we deduce as a corollary that there are no entire free time minimizers, i.e. defined on$\mathbb{R}$. This means that the Mañé set of the NewtonianN-body problem is empty.



2010 ◽  
Vol 21 (2) ◽  
pp. 297-313 ◽  
Author(s):  
Soley Ersoy ◽  
Mahmut Akyigit


2007 ◽  
Vol 2 (5) ◽  
pp. 412-418 ◽  
Author(s):  
M. Kemal Sagel . ◽  
Yilmaz Tuncer . ◽  
Yusuf Yayli .
Keyword(s):  


2007 ◽  
Vol 5 (1) ◽  
pp. 57-64 ◽  
Author(s):  
Yilmaz Tunçer ◽  
M. Kemal Sağel ◽  
Yusuf Yayli
Keyword(s):  


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