Exact Solutions of Two PDEs which Govern the 3D Inverse Problem of Dynamics

DOI10.1007/978-3-031-06632-0_12OpenAlexW4313127584MaRDI QIDQ6165062

Thomas Kotoulas

Publication date: 31 July 2023

Published in: Nonlinear Systems and Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-031-06632-0_12

zbMATH Keywords

dynamical systemspartial differential equationspotentialsinverse problem of Newtonian dynamicstwo-parametric families of orbits

Mathematics Subject Classification ID

Inverse problems for systems of particles (70F17) Hamiltonian and Lagrangian mechanics (70Hxx)

Cites Work

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• Families of planar orbits generated by homogeneous potentials
• A generalization of Szebehely's inverse problem of dynamics in dimension three
• Determination of autonomous three-dimensional force fields from a two-parameter family of orbits
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• Existence of the solution of Szebehely's equation in three dimensions using a two-parametric family of orbits
• Formulation intrinseque de l'equation de Szebehely (intrinsic formulation of Szebehely's equation)
• Construction of 3D potentials from a preassigned two-parametric family of orbits
• The energy-free equations of the 3D inverse problem of dynamics
• Inverse problem with two-parametric families of planar orbits
• Solution of the three-dimensional inverse problem
• Solution of an inverse problem of the dynamics of a particle
• Homogeneous two-parametric families of orbits in three-dimensional homogeneous potentials
• The inverse problem of dynamics: basic facts
• Two-parametric families of orbits in axisymmetric potentials

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