Vol. 93, No. 1, 1981

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Reducing the order of a Lagrangian

Richard Arens

Vol. 93 (1981), No. 1, 1–11
Abstract

Consider a Lagrangian density L defined on Rm for a system with configuration space Q. Let the order of the highest order derivatives in L be N. Then the Euler equations are generally of order 2N. We present ways of replacing L by other Lagrangian densities Lon Rm which are of order 1 and in fact linear in the derivatives. This is done by introducing roughly n times

(         )   (      )
m + N − 1     m + N
N − 1  +    N     − 2

additional variables, where n is the dimension of Q.

One of these L(denoted by L ) is such that its Euler equations have a canonical form reducing to that of Hamilton for N = m = 1.

Mathematical Subject Classification 2000
Primary: 58E30
Secondary: 49H05
Milestones
Received: 24 April 1978
Published: 1 March 1981
Authors
Richard Arens