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 L′ on Rm which
are of order 1 and in fact linear in the derivatives. This is done by introducing
roughly n times
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.
