Complex Lagrangian mechanics with constraints

TL;DR

This paper extends Lagrangian mechanics with constraints to complex manifolds, specifically Kaehlerian manifolds, exploring the nature of constraints and their holonomic properties in the complex setting.

Contribution

It introduces a complex generalization of constrained Lagrangian mechanics on Kaehlerian manifolds, analyzing the holonomic nature of constraints via closed 1-forms.

Findings

Constraints are holonomic if the 1-form is closed.

Complex Lagrangian mechanics can be formulated on Kaehlerian manifolds.

The study provides a foundation for complex constrained mechanical systems.

Abstract

In this study, it is generalized the concept of Lagrangian mechanics with constraints to complex case. To be beginning, it is considered a Kaehlerian manifold as a velocity-phase space. Then a non-holonomic constraint is given by 1-form on it. If the form is closed, it is found that the constraint is (locally) holonomic. In the result, complex analogous of some topics in constrained Lagrangian mechanical system is concluded.