To some modern readers it can appear that some dynamical quantities recognised today were used in the " Principia " but not named.
2.
In a constrained Hamiltonian system, a dynamical quantity is "'second class "'if its Poisson bracket with at least one constraint is nonvanishing.
3.
Note that it would be more natural not to start with a Lagrangian with a Lagrange multiplier, but instead take as a primary constraint and proceed through the formalism : The result would the elimination of the extraneous dynamical quantity.
4.
Variation of action with respect to the non-dynamical quantities ( t ^ a A _ a ^ i ), that is the time component of the four-connection, the shift fucntion N ^ b, and lapse function N give the constraints
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