Lagrangian vs Hamiltonian: The best approach to relativistic orbits

In introductory general relativity courses, free particle trajectories, such as astronomical orbits, are generally developed via a Lagrangian and variational calculus, so that physical examples can precede the mathematics of tensor calculus. The use of a Hamiltonian is viewed as more advanced and ty...

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Bibliographic Details
Published in:American journal of physics 2018-09, Vol.86 (9), p.678-682
Main Authors: Price, Richard H., Thorne, Kip S.
Format: Article
Language:English
Subjects:
Calculus of variations
Theory of relativity
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Summary:In introductory general relativity courses, free particle trajectories, such as astronomical orbits, are generally developed via a Lagrangian and variational calculus, so that physical examples can precede the mathematics of tensor calculus. The use of a Hamiltonian is viewed as more advanced and typically comes later if at all. We suggest here that this might not be the optimal order in a first course in general relativity, especially if orbits are to be solved with numerical methods. We discuss some of the issues that arise in both the Lagrangian and Hamiltonian approaches.
ISSN:0002-9505
1943-2909
DOI:10.1119/1.5047439