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Compatibility aspects of the method of phase synchronization for decoupling linear second-order differential equations
- Source :
- JOURNAL OF GEOMETRIC MECHANICS, Journal of Geometric Mechanics
- Publication Year :
- 2022
-
Abstract
- The so-called method of phase synchronization has been advocated in a number of papers as a way of decoupling a system of linear second-order differential equations by a linear transformation of coordinates and velocities. This is a rather unusual approach because velocity-dependent transformations in general do not preserve the second-order character of differential equations. Moreover, at least in the case of linear transformations, such a velocity-dependent one defines by itself a second-order system, which need not have anything to do, in principle, with the given system or its reformulation. This aspect, and the related questions of compatibility it raises, seem to have been overlooked in the existing literature. The purpose of this paper is to clarify this issue and to suggest topics for further research in conjunction with the general theory of decoupling in a differential geometric context.<br />Comment: 17 pages, to appear in J Geometric Mechanics
- Subjects :
- Mathematics - Differential Geometry
Second-order differential equations
linearity
Control and Optimization
Differential equation
Computer science
SEPARABILITY
FOS: Physical sciences
FORMS
phase synchronization
decoupling
SYSTEMS
FOS: Mathematics
Applied mathematics
Differential (infinitesimal)
Mathematical Physics
Physics
Applied Mathematics
Linearity
Decoupling (cosmology)
Mathematical Physics (math-ph)
Phase synchronization
Linear map
Character (mathematics)
Mathematics and Statistics
Differential Geometry (math.DG)
Mechanics of Materials
Compatibility (mechanics)
Geometry and Topology
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 19414889 and 19414897
- Database :
- OpenAIRE
- Journal :
- JOURNAL OF GEOMETRIC MECHANICS, Journal of Geometric Mechanics
- Accession number :
- edsair.doi.dedup.....57015bc37923a6f4414f96ead39c343c