(a) Consider the Lagrangian
- + (q);) +2
where Ej, ajk j,k = 1, , 1 n are constants and ajk = -akj We assume that
4j > 0, j = 1,...,n. Find the Euler-Lagrange equations and write them in the
form Äj = Fj(q,q).
(b) Compute the canonically conjugate variables Pj and obtain the Hamiltonian of the
system. Check explicitely that Hamilton's equations are equivalent to the Euler-
Lagrange equations of part (a).
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