Primary constraint
In Hamiltonian mechanics, a primary constraint is a relation between the coordinates and momenta that holds without using the equations of motion (Dirac 1964, p.8). A secondary constraint is one that is not primary, in other words it holds when the equations of motion are satisfied, but need not hold if they are not satisfied (Dirac 1964, p.14). Primary and secondary constraints were introduced by Anderson and Bergmann (1951, p.1019) and developed by Dirac (1958).
References
- Anderson, James L.; Bergmann, Peter G. (1951), "Constraints in covariant field theories", Physical Rev. (2), 83: 1018–1025, doi:10.1103/PhysRev.83.1018, MR0044382
- Dirac, P. A. M. (1958), "Generalized Hamiltonian dynamics", Proceedings of the Royal Society. London. Series A. Mathematical, Physical and Engineering Sciences, 246: 326–332, ISSN 0962-8444, MR0094205
- Dirac, P. A. M. (1958b), "The theory of gravitation in Hamiltonian form", Proceedings of the Royal Society. London. Series A. Mathematical, Physical and Engineering Sciences, 246: 333–343, ISSN 0962-8444, MR0094206
- Dirac, Paul A. M. (1964), Lectures on quantum mechanics, Belfer Graduate School of Science Monographs Series, vol. 2, Belfer Graduate School of Science, New York, MR2220894 Reprinted by Dover in 2001.
- Salisbury, D. C. (2006), Peter Bergmann and the invention of constrained Hamiltonian dynamics