Constraint systems and the Clairaut equation
نویسنده
چکیده
An extension of the Legendre transform to non-convex functions with vanishing Hessian as a mix of envelope and general solutions of the Clairaut equation is proposed. Applying this to constraint systems, the procedure of finding a Hamiltonian for a singular Lagrangian is just that of solving a corresponding Clairaut equation with a subsequent application of the proposed Legendre-Clairaut transformation. In this way the unconstrained version of Hamilton’s equations is obtained. The Legendre-Clairaut transformation presented is involutive. We demonstrate the origin of the Dirac primary constraints, along with their explicit form, and this is done without using the Lagrange multiplier method.
منابع مشابه
Constrained systems and the Clairaut equation
An extension of the Legendre transform to non-convex functions with vanishing Hessian as a mix of envelope and general solutions of the Clairaut equation is proposed. Applying this to systems with constraints, the procedure of finding a Hamiltonian for a degenerate Lagrangian is just that of solving a corresponding Clairaut equation with a subsequent application of the proposed Legendre-Clairau...
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