On the variational equations associated with a Lagrangian

Details On the variational equations associated with a Lagrangian On the variational equations associated with a Lagrangian

Oct 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980cemec..22..237h&link_type=abstract

Celestial Mechanics, vol. 22, Oct. 1980, p. 237-240.

Mathematics

1

Euler-Lagrange Equation, Numerical Stability, Variational Principles, Differential Equations, Floquet Theorem, Hamiltonian Functions, Matrices (Mathematics)

Scientific paper

The results of Broucke's study (1976) of the symplectic properties of the variational equations for a particular Lagrangian form using constant coefficients are generalized for the case of an arbitrary Lagrangian. It is shown that the characteristic exponents of a periodic solution can be computed in Lagrangian formulation. Moreover, it is valid for any arbitrary transformation of (q,p) to some other noncanonical variables in phase space, and the eigenvalues of the monodromy matrix are not changed at the end of each complete revolution of the periodic solution.

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