Particular solutions of the Hamilton–Jacobi equation and their usage

Particular solutions of the Hamilton–Jacobi equation and their usage

We show the possibility of using particular solutions of the Hamilton–Jacobi equation in problems of qualitative analysis of Lagrangian systems with cyclic first integrals. We present a procedure for finding and studying invariant manifolds of such systems. The efficiency of the suggested approach i...

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Veröffentlicht in:Differential equations 2016-03, Vol.52 (3), p.292-305
Hauptverfasser: Irtegov, V. D., Titorenko, T. N.
Format: Artikel
Sprache:eng
Schlagworte:
Control theory
Difference and Functional Equations
Differential equations
Hamilton-Jacobi equation
Integrals
Invariants
Lagrange multiplier
Manifolds
Mathematical analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Qualitative analysis
Studies
Topological manifolds
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Beschreibung
Zusammenfassung:We show the possibility of using particular solutions of the Hamilton–Jacobi equation in problems of qualitative analysis of Lagrangian systems with cyclic first integrals. We present a procedure for finding and studying invariant manifolds of such systems. The efficiency of the suggested approach is illustrated by examples of the solution of specific problems.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266116030046