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The distinction between primary and secondary constraints is not a very fundamental one. It depends very much on the original
Lagrangian which we start off with. Once we have gone over to the Hamiltonian formalism, we can really forget about the distinction between primary and secondary constraints.
73:. A few authors use more refined terminology, where the non-primary constraints are divided into secondary, tertiary, quaternary, etc. constraints. The secondary constraints arise directly from the condition that the primary constraints are preserved by
68:
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 The secondary constraints arise from the condition that the primary constraints should be preserved in
77:, the tertiary constraints arise from the condition that the secondary ones are also preserved by time, and so on. Primary and secondary constraints were introduced by Anderson and
88:. These divisions are independent: both first- and second-class constraints can be either primary or secondary, so this gives altogether four different classes of constraints.
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Anderson, James L.; Bergmann, Peter G. (1951). "Constraints in covariant field theories".
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The terminology of primary and secondary constraints is confusingly similar to that of
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381:(1246): 333–343.
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241:(1950).
138:(1964).
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