Hello, this doubt is related to Generalized Hamiltonian Dynamics paper by Dirac.(adsbygoogle = window.adsbygoogle || []).push({});

Consider the set of n equations : p_{i}= [itex]\partial[/itex]L/[itex]\partial[/itex]v_{i},

(where v_{i}is q_{i}(dot) = dq_{i}/dt, or time derivative of q_{i})(L is the lagrangian, q represent degrees of freedom in configuration space)

Now Dirac says : "If the n quantities [itex]\partial[/itex]L/[itex]\partial[/itex]v_{n}on the right-hand side of the given equations are NOT independent functions of the velocities, we can eliminate the v's from (the above-given) set of equations and obtain one or more equations:

∅_{j}(q, p) = 0, (j = 1, 2, ... ,m if there are m such constraints)"

Could anyone please explain how this comes about? I can't understand how the v's can be necessarily eliminated, and if the p's are not all independent, then we can simply obtain relations like Ʃa_{i}p_{i}= 0 (where a's are non-zero coefficients), not involving q's at all.

Thanks.

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# Eliminating velocities from Lagrange E.o.M

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