Primary constraint

Not to be confused with first class 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).

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
• Salisbury, D. C. (2006), Peter Bergmann and the invention of constrained Hamiltonian dynamics
• 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.