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In this chapter, after recalling Newton’s laws of dynamics, we start by discussing the integrals of motion and by providing the elliptic solution of Kepler’s problem. Then, we introduce the Laplace-Runge-Lenz vector, we shortly describe parabolic and hyperbolic motions and we present the Hamiltonian formulation of Kepler’s problem in terms of the so-called action-angle Delaunay variables. Finally, we discuss some properties of Kepler’s problem under the dissipative effect due to a generalized Stokes drag.

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Kepler’s Problem

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  • 发表日期：

    2025年

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  • Alessandra Celletti

摘要

In this chapter, after recalling Newton’s laws of dynamics, we start by discussing the integrals of motion and by providing the elliptic solution of Kepler’s problem. Then, we introduce the Laplace-Runge-Lenz vector, we shortly describe parabolic and hyperbolic motions and we present the Hamiltonian formulation of Kepler’s problem in terms of the so-called action-angle Delaunay variables. Finally, we discuss some properties of Kepler’s problem under the dissipative effect due to a generalized Stokes drag.