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Origin and infinity manifolds for mechanical systems with homogeneous potentials

Origin and infinity manifolds for mechanical systems with homogeneous potentials We study manifolds describing the behavior of motions close to the origin and at infinity of configuration space, for mechanical systems with homogeneous potentials. We find an inversion between these behaviors when the sign of the degree of homogeneity is changed. In some cases, the blow up equations can be written in canonical form, by first reducing to a contact structure. A motivation for the use of blow-up techniques is given, and some examples are studied in detail. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Origin and infinity manifolds for mechanical systems with homogeneous potentials

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References (19)

Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/BF00140121
Publisher site
See Article on Publisher Site

Abstract

We study manifolds describing the behavior of motions close to the origin and at infinity of configuration space, for mechanical systems with homogeneous potentials. We find an inversion between these behaviors when the sign of the degree of homogeneity is changed. In some cases, the blow up equations can be written in canonical form, by first reducing to a contact structure. A motivation for the use of blow-up techniques is given, and some examples are studied in detail.

Journal

Acta Applicandae Mathematicae – Springer Journals

Published: Jun 9, 2004

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