Generalized Hamiltonian dynamics

@article{Dirac1958GeneralizedHD,
  title={Generalized Hamiltonian dynamics},
  author={Paul Adrien Maurice Dirac},
  journal={Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences},
  year={1958},
  volume={246},
  pages={326 - 332}
}
  • P. Dirac
  • Published 19 August 1958
  • Physics
  • Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
The author’s procedure for passing from the Lagrangian to the Hamiltonian when the momenta are not independent functions of the velocities is put into a simpler and more practical form, the main results being obtained by a direct solution of the equations provided by the consistency requirements. It is shown how, under certain conditions, one can eliminate some of the degrees of freedom and so make a substantial simplification in the Hamiltonian formalism. 
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References

SHOWING 1-4 OF 4 REFERENCES
Homogeneous variables in classical dynamics
The well-known methods of classical mechanics, based on the use of a Lagrangian or Hamiltonian function, are adequate for the treatment of nearly all dynamical systems met with in practice. There
Forms of Relativistic Dynamics
For the purposes of atomic theory it is necessary to combine the restricted principle of relativity with the Hamiltonian formulation of dynamics. This combination leads to the appearance of ten
Dirac, Homogeneous variables in classical dynamics
  • Proc. Camb. Phil. Soc, vol
  • 1933