Minimally classifying relative equilibria
نویسندگان
چکیده
منابع مشابه
Minimally Classifying Relative Equilibria
Estimates on a minimal classification o f relative equilibria in the planar n-body problem of celestial mechanics have been announced in [1], [2]. Our main theorem asserts that these estimates are actually met for any n > 3 on an open set in IR~_. For any n > 4, this open set is proper.
متن کاملClassifying Relative Equilibria
We announce several theorems which suggest a minimal classification of relative equilibria in the planar «-body problem. These theorems also answer several questions on the nature of degenerate relative equilibria classes which were asked recently by S. Smale [3]. A summary of previous results can be found in an earlier paper [1]. It is a pleasure to thank S. Smale for encouragement in this work.
متن کاملStabilization of relative equilibria
This paper discusses the problem of obtaining feedback laws to asymptotically stabilize relative equilibria of mechanical systems with symmetry. We show how to stabilize an internally unstable relative equilibrium using internal actuators. The methodology is that of potential shaping, but the system is allowed to be underactuated, i.e., have fewer actuators than the dimension of the shape space...
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We describe a method for finding the families of relative equilibria of molecules which bifurcate from an equilibrium point as the angular momentum is increased from 0. Relative equilibria are steady rotations about a stationary axis during which the shape of the molecule remains constant. We show that the bifurcating families correspond bijectively to the critical points of a function h on the...
متن کاملStabilization of Relative Equilibria II
In this paper, we obtain feedback laws to asymptotically stabilize relative equilibria of mechanical systems with symmetry. We use a notion of stability ‘modulo the group action’ developed by Patrick [1992]. We deal with both internal instability and with instability of the rigid motion. The methodology is that of potential shaping, but the system is allowed to be internally underactuated, i.e....
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ژورنال
عنوان ژورنال: Letters in Mathematical Physics
سال: 1977
ISSN: 0377-9017,1573-0530
DOI: 10.1007/bf01793953