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I am looking for a proof of the next theorem:

"If the higher order time derivative Lagrangian is non-degenerate, there is at least one linear instability in the Hamiltonian of this system."

Where Non-degeneracy means that the highest time derivative term can be expressed in terms of canonical variables.

Improve this question
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    $\begingroup$ Related: genneth's answer to this Phys.SE question. $\endgroup$
    – Qmechanic ♦
    Commented Jan 1, 2015 at 11:37
  • $\begingroup$ I prefer a reference where the theorem and its proof is discussed therein. $\endgroup$
    – MathematicalPhysicist
    Commented Jan 1, 2015 at 13:21
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    $\begingroup$ I believe this answers your question. $\endgroup$
    – Praful Gagrani
    Commented Mar 21, 2016 at 17:53

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