Titlebook: Dynamics through First-Order Differential Equations in the Configuration Space; Jaume Llibre,Rafael Ramírez,Valentín Ramírez Book 2023 The

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,Cartesian-Synge–Cinsov Vector Field,We shall study the autonomous mechanical system with configuration space

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Vincent E. Rubatzky,Mas Yamaguchienerated by a smooth Hamiltonian over a symplectic manifold. The flows are symplectomorphisms, i.e., a transformation of phase space that is volume preserving and preserves the symplectic structure of the phase space, and hence obeys Liouville’s Theorem. In 1973 Yoichiro Nambu suggested an extension

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978-3-031-27097-0The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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,Generalized Cartesian–Nambu Vector Fields,ven Poisson bracket and replacing a single Hamiltonian . for . − 1 Hamiltonian ., …, .. In the canonical Hamiltonian formulation the equations of motion (Hamilton equations) are defined via the Poisson bracket.

Magisterial

dy of ODEs.Offers a solution to the inverse problem in celesThe goal of this monograph is to answer the question, is it possible to solve the dynamics problem inside the configuration space instead of the phase space? By introducing a proper class of vector field – the Cartesian vector field – given

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Book 2023 space? By introducing a proper class of vector field – the Cartesian vector field – given in a Riemann space, the authors explore the connections between the first order ordinary differential equations (ODEs) associated to the Cartesian vector field in the configuration space of a given mechanical

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