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Separable Systems of Coordinates for Triangular Newton Equations
Author(s) -
Marciniak Krzysztof,
RauchWojciechowski Stefan
Publication year - 2007
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2007.00363.x
Subject(s) - mathematics , quadratic equation , separable space , bipolar coordinates , quadric , mathematical analysis , parabolic coordinates , motion (physics) , log polar coordinates , action angle coordinates , local coordinates , orthogonal coordinates , property (philosophy) , pure mathematics , geometry , classical mechanics , physics , philosophy , epistemology
Triangular form of Newton equations is a strong property. Together with the existence of a single quadratic with respect to velocities integral of motion, it usally implies existence of further n − 1 integrals that are also quadratic. These integrals make the triangular system separable in new type of coordinates. The separation coordinates are built of quadric surfaces that are nonorthogonal and noconfocal and can intersect along lower dimensional singular manifolds. We present here separability theory for n ‐dimensional triangular systems and analyze the structure of separation coordinates in two and three dimensions.