Constrained 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 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-Clairaut transformation. In this way the unconstrained version of Hamiltonian equations is obtained. The LegendreClairaut 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
Constraint 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 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 transf...
متن کاملPositive solution of non-square fully Fuzzy linear system of equation in general form using least square method
In this paper, we propose the least-squares method for computing the positive solution of a $mtimes n$ fully fuzzy linear system (FFLS) of equations, where $m > n$, based on Kaffman's arithmetic operations on fuzzy numbers that introduced in [18]. First, we consider all elements of coefficient matrix are non-negative or non-positive. Also, we obtain 1-cut of the fuzzy number vector solution of ...
متن کاملSingular constrained linear systems
In the linear system Ax = b the points x are sometimes constrained to lie in a given subspace S of column space of A. Drazin inverse for any singular or nonsingular matrix, exist and is unique. In this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of Drazin inverse in solving such systems is investigated. Constrained linear system arise ...
متن کاملA chance-constrained multi-objective model for final assembly scheduling in ATO systems with uncertain sub-assembly availability
A chance-constraint multi-objective model under uncertainty in the availability of subassemblies is proposed for scheduling in ATO systems. The on-time delivery of customer orders as well as reducing the company's cost is crucial; therefore, a three-objective model is proposed including the minimization of1) overtime, idletime, change-over, and setup costs, 2) total dispersion of items’ deliver...
متن کاملConstrained Controller Design for Real-time Delay Recovery in Metro Systems
This study is concerned with the real-time delay recovery problem in metro loop lines. Metro is the backbone of public transportation system in large cities. A discrete event model for traffic system of metro loop lines is derived and presented. Two effective automatic controllers, linear quadratic regulator (LQR) and model predictive controller (MPC), are used to recover train delays. A newly-...
متن کامل