Geometric and physical interpretation of the action principle

We give a geometric interpretation for the principle of stationary action in classical Lagrangian particle mechanics. In a nutshell, the difference of the action along a path and its variation effectively “counts” the possible evolutions that “go through” the area enclosed. If the path corresponds t...

Full description

Saved in:
Bibliographic Details
Published in:Scientific reports 2023-07, Vol.13 (1), p.12138-12138, Article 12138
Main Authors: Carcassi, Gabriele, Aidala, Christine A.
Format: Article
Language:English
Subjects:
639/705/1041
639/766
Calculus
Charged particles
Determinism
Dynamical systems
Evolution
Geometry
Humanities and Social Sciences
Kinematics
Magnetic fields
Mechanics
multidisciplinary
Physics
Science
Science (multidisciplinary)
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We give a geometric interpretation for the principle of stationary action in classical Lagrangian particle mechanics. In a nutshell, the difference of the action along a path and its variation effectively “counts” the possible evolutions that “go through” the area enclosed. If the path corresponds to a possible evolution, all neighbouring evolutions will be parallel, making them tangent to the area enclosed by the path and its variation, thus yielding a stationary action. This treatment gives a full physical account of the geometry of both Hamiltonian and Lagrangian mechanics which is founded on three assumptions: determinism and reversible evolution, independence of the degrees of freedom and equivalence between kinematics and dynamics. The logical equivalence between the three assumptions and the principle of stationary action leads to a much cleaner conceptual understanding.
ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-023-39145-y