Hamilton-Jacobi quantization of singular Lagrangians with linear   velocities
  In this paper, constrained Hamiltonian systems with linear velocities are investigated by using the Hamilton-Jacobi method. We shall consider the integrablity conditions on the equations of motion and the action function as well in order to obtain the path integral quantization of singular Lagrangians with linear velocities. 
Sami I. Muslih, Hosam A. El-Zalan, Eqab M. Rabei