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2 years ago in Mathematics , Theoretical Physics By Vishal

How can singular Lagrangian systems be analyzed geometrically?

I'm working with a class of constrained systems where the standard Legendre transformation fails, leading to a singular Lagrangian. In my research, I need a robust geometric framework to properly derive the equations of motion and understand the inherent constraints and gauge structures.

SingularLagrangians GeometricMechanics

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By Pravin Patel Answered 2 years ago

From my work in geometric mechanics, I've seen that singular Lagrangians require moving beyond the standard Hamiltonian framework. I would recommend starting with the Gotay-Nester algorithm, which uses presymplectic geometry on the constraint manifold. The key is to systematically handle the primary and secondary constraints that arise from the Lagrangian's singularity. This geometric approach cleanly separates gauge freedoms from physical dynamics and leads to a well-defined, if constrained, phase space. It’s a powerful method for quantizing gauge theories.

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How can singular Lagrangian systems be analyzed geometrically?

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