Lagrangian formalism for nonlinear second-order Riccati systems: One-dimensional integrability and two-dimensional superintegrability
作者： José F. Cariñena , Mariano Santander , Manuel F. Rañada
DOI: 10.1063/1.1920287
关键词: Riccati equation 、 Algebraic Riccati equation 、 Ordinary differential equation 、 Lagrangian 、 Lissajous curve 、 Mathematics 、 Nonlinear system 、 Formalism (philosophy of mathematics) 、 Nonlinear oscillators 、 Mathematical analysis
摘要: The existence of a Lagrangian description for the second-order Riccati equation is analyzed and results are applied to study two different nonlinear systems both related with generalized equation. Lagrangians non-natural forces not derivable from potential. constant value E preserved energy function can be used as an appropriate parameter characterizing behavior solutions these systems. In second part two-dimensional versions endowed superintegrability proved. explicit expressions additional integrals obtained in cases. Finally it proved that orbits system, represents oscillator, considered Lissajous figures
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