| Abstract: |
| For $N=3$, it is well known that on the Euclidean space there are exactly five relative equilibria: three collinear (Euler relative equilibria) and two planar relative equilibria forming an equilateral triangle (Lagrange relative equilibria).
What happen when we curved the Euclidian space in positive or negative way?
The big difficulty to study relative equilibria on these spaces, that we call $RE$ by short, is the absence of the center of mass as a first integral, since many of the standard methods used in the classical case don`t apply any more.
In this talk we will show a geometrical method to study $RE$ on these spaces, when the particles are moving under the influence of a general potential which only depends on the mutual distances among the masses.
In particular we will show how to determine the rotation axis, which is a big obstacle to obtain $RE$. We restrict our analysis to
the case $N=3$, where we give some new families of Euler and Lagrange $RE$ on the sphere for the cotangent potential (the natural extension of the Newtonian potential to the sphere). |
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