... ¨qi(t0) if we can invert∂2L∂ ˙qi∂ ˙qj.Thus, if a constraint occurs, ¨qi(t0) cannot be determined from the initial conditions using1.4. DIRAC’S THEORY OF CONSTRAINTS 11Lagrange’s ... secondary. We could in principle also have tertiaryconstraints, etc (In practice, tertiary constraints don’t arise).Suppose we have constraints χi. They can be divided into First class and ... DIRAC’S THEORY OF CONSTRAINTS 13fixes ai, bi, ci(All arbitrariness is eliminated).Dirac Brackets (designed to replace Poisson Brackets so as to eliminate all constraintsfrom the theory) .Note:[θi,...