Jacobi integral: A real-world application of the Lagrangian formulation

Jeremy A. Riousset; Manasvi Lingam

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arXiv · 2312.15800

Jacobi integral: A real-world application of the Lagrangian formulation

Jeremy A. Riousset·Manasvi Lingam

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Abstract

The applicability of advanced classical mechanics (viz., the Lagrangian and/or Hamiltonian approaches) to real-world problems may not always seem straightforward, despite the mathematical rigor and elegance of this field. Here, we present a proof of the Jacobi integral using the Lagrangian formulation as a viable alternative to the usual demonstration using Newton's second law. The result represents a useful example of how advanced classical mechanics can provide a significant advantage over standard methods (i.e., Newton's laws). We conclude with an illustration of the Jacobi integral in our Solar system: the Circular Restricted 3-Body Problem (CR3BP) around Pluto and Charon.

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Jeremy A. Riousset, Manasvi Lingam. 2023-12-25. Jacobi integral: A real-world application of the Lagrangian formulation. https://arxiv.org/abs/2312.15800

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