An Investigation of Singular Lagrangians as Field Systems

TL;DR

This paper explores the relationship between singular Lagrangians as field systems and the general approach, demonstrating their equivalence and analyzing specific examples including a zero-rank Hessian case.

Contribution

It establishes that singular Lagrangians as field systems are always consistent with the general approach and clarifies the nature of constraints and equations of motion.

Findings

Singular Lagrangians as field systems align with the general approach.

Equivalence of equations of motion and constraints in both treatments.

Analysis of a singular Lagrangian with zero-rank Hessian matrix.

Abstract

The link between the treatment of singular lagrangians as field systems and the general approch is studied. It is shown that singular Lagrangians as field systems are always in exact agreement with the general approch. Two examples and the singular Lagrangian with zero rank Hessian matrix are studied. The equations of motion in the field systems are equivalent to the equations which contain accleration, and the constraints are equivalent to the equations which do not contain acceleration in the general approch treatment.