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

2023/12/25 by Riousset, Jeremy A., Lingam, Manasvi
#Classical Physics (physics.class-ph) #FOS: Physical sciences

paper · doi:10.48550/arxiv.2312.15800

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.

Related

• Jacobi's Action and the Density of States
• Does a Good Conservation of Jacobi's Constant Imply a Good Orbital Numerical Integration?: I. Resonant Orbits
• Singular lagrangians and the Hamilton-Jacobi formalism in classical mechanics
• Physical Consequences of the Jacobi Identity
• Constants of the Motion in a Gravitational Field and the Hamilton-Jacobi Function