The Dirac-Hamiltonian formalism and the realization of constraints by small masses (Q2761254)

On a \(2n\)-dimensional manifold \(M\), the author considers a Hamiltonian system with Hamiltonian \(H = H_0(p,q,Q)+\frac{P^2}{2\varepsilon} + \varepsilon H_1(p,q,Q,\varepsilon)\), where \(\varepsilon>0\) is small parameter, and \(H_0\) is non-degenerate with respect to impulses \(p\), \(\{p,q\}\in \mathbb{R}^{2n-2}\). The author employs the generalized Dirac-Hamiltonian formalism [\textit{P. A. M. Dirac}, Can. J. Math. 2, No. 2, 129-148 (1950; Zbl 0036.14104)] and shows that when the mass tends to zero under certain initial conditions, the limiting motions exist and match the motions of the Hamiltonian system with constraints.