To see the consequences of having each constraint be a constant of the motion, take, for example H ˙ ˙ 1 = { H 1 , H } = λ λ 1 { H 1 , H 1 } + { H 1 , λ λ 1 } H 2 + λ λ 2 { H 2 , H 1 } + { λ λ 2 , H 1 } H 2 .