Treatment of Holonomic Constraints as Regular Systems

Dr. Khaled  Nawafleh

Abstract

In this work we treat holonomic constraints as a singular system. We discuss how to transform this singular system into a regular one. The formalism described here relies on the possibility of replacing the holonomic constraints in the singular Lagrangian with their time derivatives which is equivalent to the first consistency condition in Dirac^,s method. The new constructed Lagrangian becomes regular in an extended phase space which can be treated using standard methods. This enables us to formulate the Hamiltonian for holonomic constraints, and the equations of motion can be obtained from this Hamiltonian.